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Patera, Jiri

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Professeur titulaire

Faculté des arts et des sciences - Département de mathématiques et de statistique

André-Aisenstadt local 4441

514 343-6419

Courriels

Affiliations

  • Membre - CRM — Centre de recherches mathématiques

Expertises

Les nouvelles recherches que nous effectuons en quasicristallographie représente depuis peu une part importante de l'ensemble de nos recherches.

Encadrement Tout déplier Tout replier

Choix d'un associateur 2-D pour le balayage multiple et optimisation de l'estimation des pistes Thèses et mémoires dirigés / 2009
Moreau, Francis
Abstract
Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Families of orthogonal functions defined by the Weyl groups of compact Lie groups Thèses et mémoires dirigés / 2012-08
Hakova, Lenka
Abstract
Plusieurs familles de fonctions spéciales de plusieurs variables, appelées fonctions d'orbites, sont définies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algèbres de Lie simples. Ces fonctions sont étudiées depuis près d'un siècle en raison de leur lien avec les caractères des représentations irréductibles des algèbres de Lie simples, mais également de par leurs symétries et orthogonalités. Nous sommes principalement intéressés par la description des relations d'orthogonalité discrète et des transformations discrètes correspondantes, transformations qui permettent l'utilisation des fonctions d'orbites dans le traitement de données multidimensionnelles. Cette description est donnée pour les groupes de Weyl dont les racines ont deux longueurs différentes, en particulier pour les groupes de rang $2$ dans le cas des fonctions d'orbites du type $E$ et pour les groupes de rang $3$ dans le cas de toutes les autres fonctions d'orbites.

Brisure de symétrie par la réduction des groupes de Lie simples à leurs sous-groupes de Lie réductifs maximaux Thèses et mémoires dirigés / 2012-12
Larouche, Michelle
Abstract
Dans ce travail, nous exploitons des propriétés déjà connues pour les systèmes de poids des représentations afin de les définir pour les orbites des groupes de Weyl des algèbres de Lie simples, traitées individuellement, et nous étendons certaines de ces propriétés aux orbites des groupes de Coxeter non cristallographiques. D'abord, nous considérons les points d'une orbite d'un groupe de Coxeter fini G comme les sommets d'un polytope (G-polytope) centré à l'origine d'un espace euclidien réel à n dimensions. Nous introduisons les produits et les puissances symétrisées de G-polytopes et nous en décrivons la décomposition en des sommes de G-polytopes. Plusieurs invariants des G-polytopes sont présentés. Ensuite, les orbites des groupes de Weyl des algèbres de Lie simples de tous types sont réduites en l'union d'orbites des groupes de Weyl des sous-algèbres réductives maximales de l'algèbre. Nous listons les matrices qui transforment les points des orbites de l'algèbre en des points des orbites des sous-algèbres pour tous les cas n<=8 ainsi que pour plusieurs séries infinies des paires d'algèbre-sous-algèbre. De nombreux exemples de règles de branchement sont présentés. Finalement, nous fournissons une nouvelle description, uniforme et complète, des centralisateurs des sous-groupes réguliers maximaux des groupes de Lie simples de tous types et de tous rangs. Nous présentons des formules explicites pour l'action de tels centralisateurs sur les représentations irréductibles des algèbres de Lie simples et montrons qu'elles peuvent être utilisées dans le calcul des règles de branchement impliquant ces sous-algèbres.

Special functions of Weyl groups and their continuous and discrete orthogonality Thèses et mémoires dirigés / 2014-04
Motlochova, Lenka
Abstract
Cette thèse s'intéresse à l'étude des propriétés et applications de quatre familles des fonctions spéciales associées aux groupes de Weyl et dénotées $C$, $S$, $S^s$ et $S^l$. Ces fonctions peuvent être vues comme des généralisations des polynômes de Tchebyshev. Elles sont en lien avec des polynômes orthogonaux à plusieurs variables associés aux algèbres de Lie simples, par exemple les polynômes de Jacobi et de Macdonald. Elles ont plusieurs propriétés remarquables, dont l'orthogonalité continue et discrète. En particulier, il est prouvé dans la présente thèse que les fonctions $S^s$ et $S^l$ caractérisées par certains paramètres sont mutuellement orthogonales par rapport à une mesure discrète. Leur orthogonalité discrète permet de déduire deux types de transformées discrètes analogues aux transformées de Fourier pour chaque algèbre de Lie simple avec racines des longueurs différentes. Comme les polynômes de Tchebyshev, ces quatre familles des fonctions ont des applications en analyse numérique. On obtient dans cette thèse quelques formules de <<cubature>>, pour des fonctions de plusieurs variables, en liaison avec les fonctions $C$, $S^s$ et $S^l$. On fournit également une description complète des transformées en cosinus discrètes de types V--VIII à $n$ dimensions en employant les fonctions spéciales associées aux algèbres de Lie simples $B_n$ et $C_n$, appelées cosinus antisymétriques et symétriques. Enfin, on étudie quatre familles de polynômes orthogonaux à plusieurs variables, analogues aux polynômes de Tchebyshev, introduits en utilisant les cosinus (anti)symétriques.

Décomposition des produits de fonctions d'orbites symétriques et antisymétriques des groupes de Weyl Thèses et mémoires dirigés / 2006
Dubois, Valérie
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Modélisation et intégration du contexte dans le cadre de la détection de cibles en imagerie radar Thèses et mémoires dirigés / 2006
Bonneau, Olivier
Abstract
Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Projets de recherche Tout déplier Tout replier

Hard and soft information fusion to aid situation understanding OODA Technologies inc. , CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2018 - 2019

Fourier transforms on multidimensional lattices and their exploitation in physics CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2016 - 2022

Centre de recherches mathematiques (crm) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2015 - 2022

(bourse zofia grabowiecka) exploitation of special functions orthogonal on finite domains of 2d and 3d lattices-fourier expansions of functions sampled on lattices FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2014 - 2014

(bourse lenka motlochova) exploitation of special functions orthogonal on finite domains of 2d and 3d lattices-fourier expansions of functions sampled on lattices FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2013 - 2015

(bourse marzena szajewska) exploitation of special functions orthogonal on finite domains of 2d and 3d lattices-fourier expansions of functions sampled on lattices FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2013 - 2015

Computational resources for research in mathematics and statistics CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2013 - 2015

Exploitation of special functions orthogonal on finite domains of 2d and 3d lattices-fourier expansions of functions sampled on lattices Innovation, Sciences et Développement économique Canada / 2013 - 2015

(bourse agnieszka maria tereszkiewick qui remplace olivier rouch pour le deuxieme stage) development of algorithms and methods for fusion of imprecise information FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2013

Development of lagorithms and methods for fusion of imprecise information FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2012 - 2013

Symmetries in physics applications CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 2011 - 2015

Development of algorithms and methods for fusion of imprecise information OODA Technologies inc. / 2011 - 2013

Reseau mitacs // development of algorithms and methods for fusion of imprecise information Secrétariat Inter-Conseil et Réseaux des centres d'excellence (RCE) / 2011 - 2013

New orthogonal polynomials and their applications OODA Technologies inc. / 2011 - 2012

Development of algorithms and methods for information fusion enabled decision support OODA Technologies inc. / 2011 - 2011

Centre de recherches mathematiques (crm) FRQNT/Fonds de recherche du Québec - Nature et technologies (FQRNT) / 2008 - 2016

Symmetries in physics applications CRSNG/Conseil de recherches en sciences naturelles et génie du Canada (CRSNG) / 1994 - 2017

Publications choisis Tout déplier Tout replier

Gaussian cubature arising from hybrid characters of simple Lie groups

R.V. Moody, L. Motlochova, J. Patera, Gaussian cubature arising from hybrid characters of simple Lie groups , pp 20 (2014), accepted in, J. Fourier Analysis and its Applications

Polytope contractions within icosahedral symmetry

M. Bodner, J. Patera, M. Szajewska, Polytope contractions within icosahedral symmetry , pp 10 (2014), accpeted in, Canadian Journal of Physics

Breaking of icosahedral Symmetry: C60 to C70

M. Bodner, J. Patera, M. Szajewska, Breaking of icosahedral Symmetry: C60 to C70 9(3), (2014), , PLoS ONE

Icosahedral symmetry breaking: C60 to C78, C96 and to related nanoutubes, Acta Crystallographica (A70)

M. Bodner, E. Bourret, J. Patera, M. Szajewska, Icosahedral symmetry breaking: C60 to C78, C96 and to related nanoutubes, Acta Crystallographica (A70) , (2014), , Foundations of Crystallography

Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2

F. Lemire, J. Patera, M. Szajewska, Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2 , (2014), 10.1007/s10773-014-2444-7, International Journal of theoretical Physics

Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2

Lemire F., Patera J. et Szajewska M., Dominant weight multiplicities in hybrid characters of Bn, Cn, F4, G2 10.1007/s10773-014-2444-7, (2014), , International Journal of Theoretical Physics

Icosahedral symmetry breaking: C60 to C78, C96 and to related nanotubes

Bodner M., Bourret E., Patera J. et Szajewska M., Icosahedral symmetry breaking: C60 to C78, C96 and to related nanotubes 6, 650-655 (2014), , Acta Crystallographica(A70)

C70, C80, C90, and carbon nanotubes by breaking of the icosahedral symmetry of C60

M. Bodner, J. Patera, M. Szajewska, C70, C80, C90, and carbon nanotubes by breaking of the icosahedral symmetry of C60 69(6), (2013), , Acta Crystallographica Section A: Foundation of Crystallography

Four families of Weyl group orbit functions of B3 and C3

L. Hakova, J. Hrivnak, J. Patera, Four families of Weyl group orbit functions of B3 and C3 54, (2013), , J. Math. Physics

On generalizing the Shmushkevich method

M. Bodner, G. Chadzitaskos, J. Patera, A. Tereszkiewicz, On generalizing the Shmushkevich method 53(5), (2013), , Acta Polytechnica

Four families of Weyl group orbit functions of $B_3$ and $C_3$

Hàkovà, Lenka, Hrivnàk, Ji\v rí et Patera, Ji\v rí, Four families of Weyl group orbit functions of $B_3$ and $C_3$ 54, 083501, 19 (2013), , J. Math. Phys.

Six types of E-functions of the Lie groups O(5) and G(2)

L. Hakova, J. Hrivnak, J. Patera, Six types of E-functions of the Lie groups O(5) and G(2) 45, (2012), , J. Phys. A: Math Theor.

On Discretization of Tori of Compact Simple Lie Groups II

J. Hrivnak, L. Motlochova, J. Patera, On Discretization of Tori of Compact Simple Lie Groups II 45, (2012), , J. Phys. A: Math. Theor.

Three-variable exponentiol functions of the alternating group

J. Hrivnak, J. Patera, S. Posta, Three-variable exponentiol functions of the alternating group 45, (2012), , J. Phys. A: Math. Theor.

Affine reflection groups for tiling applications: knot thoery and DNA

M. Boder, J. Patera, M. Peterson, Affine reflection groups for tiling applications: knot thoery and DNA 53, (2012), , J. Math. Phys.

Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups

Moody, Robert V. et Patera, Ji\v rí, Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups 47, 509--535 (2011), , Adv. in Appl. Math.

Centralizers of maximal regular subgroups of compact simple Lie groups

M. Larouche, F.W. Lemire, J. Patera, Centralizers of maximal regular subgroups of compact simple Lie groups 44, (2011), , J. Phys. A: Math. Theor.

On E-functions of semisimple Lie algebras

J. Hrivnak, I. Kashuba, J. Patera, On E-functions of semisimple Lie algebras 44, (2011), , J. Phys. A: Math. Theor.

Branching rules for Weyl group orbits of simple Lie Algebras Bn and Dn

M. Larouche, J. Patera, Branching rules for Weyl group orbits of simple Lie Algebras Bn and Dn 44, (2011), , J. Phys. A: Math. Theor.

Orthogonal polynomials of compact simple Lie groups

Nesterenko, Maryna, Patera, Ji\v rí et Tereszkiewicz, Agnieszka, Orthogonal polynomials of compact simple Lie groups Nesterenko, Maryna and Patera, Ji\v rí and Tereszkiewicz, Agnieszka, Art. ID 969424, 23 (2011), , Int. J. Math. Math. Sci.

Orthogonal polynomials of compact simple Lie groups. The branching rules for polynomials

M. Nesterenko, J. Patera, M. Szajewska, A. Tereszkiewicz, Orthogonal polynomials of compact simple Lie groups. The branching rules for polynomials 43, (2010), , J. Phys. A: Math. Theor.

Two-dimensional symmetric and antisymmetric generalizations of sine functions

J. Hrivnak, L. Motlochova, J. Patera, Two-dimensional symmetric and antisymmetric generalizations of sine functions 51, (2010), , J. Math. Phys.

On E-discretization of tori of compact simple Lie groups

J. Hrivnak, J. Patera, On E-discretization of tori of compact simple Lie groups 43, (2010), , J. Phys. A: Math. Thoer.

Two dimensional symmetric and antisymmetric generalizations of exponential and cosine functions

J. Hrivnak, J. Patera, Two dimensional symmetric and antisymmetric generalizations of exponential and cosine functions 51, (2010), , J. Math. Phys.

Tereszkiewicz, Orbit functions of SU(n) and Chebyshev polynomials

M. NESTERENKO, J. PATERA, Tereszkiewicz, Orbit functions of SU(n) and Chebyshev polynomials , (2010), , Group Analysis of Differential Équations and Integrable Systems, Protaras, Cyprus

Quasicrystal models in cryptography in Geometric Methods in Physics

M. NESTERENKO, J. PATERA, Quasicrystal models in cryptography in Geometric Methods in Physics , 148-159 (2009), , APS Conference Proceedings 1191

Discretization of tori of exceptional simple Lie algebras

J. HRIVNAK, J. PATERA, Discretization of tori of exceptional simple Lie algebras , 110-115 (2009), , Geometric Methods in Physics, APS Conference Proceedings 1191

Invariants of Lie algebras via moving frame approach

V. BOYKO, J. PATERA, R. POPOVYCH, Invariants of Lie algebras via moving frame approach , 36-44 (2009), , Group Analysis of Differential Équations and Integrable Systems, Protaras, Cyprus

On orbit functions, their properties and applications

M. NESTERENKO, J. PATERA, On orbit functions, their properties and applications , 155-163 (2009), , Group Analysis of Differential Équations and Integrable Systems, Protaras, Cyprus

Alternating group and multivariate exponential functions

Klimyk A.U. et Patera J., Alternating group and multivariate exponential functions , 233-246 (2009), , Neolithic Scots to John McKay AMS-CRM Proceedings and Lectures Notes Series

Branching rules for the Weyl group orbits of the Lie algebra A_n

Larouche, M., Nesterenko, M. et Patera, J., Branching rules for the Weyl group orbits of the Lie algebra A_n 42, 485203, 15 (2009), , J. Phys. A

On discretization of tori of compact simple Lie groups

J. Hrivnak, J. Patera, On discretization of tori of compact simple Lie groups 42, 385208, 26 (2009), , J. Phys. A

Discretization of compact semisimple Lie groups

J. HRIVNAK, J. PATERA, Discretization of compact semisimple Lie groups , 196-202 (2008), , Geometric Methods in Physics, AIP Conf. Proc. 1079

Quasicrystals in cryptography, in Aspects of Network and information Security

M. NESTERENKO, J. PATERA, Quasicrystals in cryptography, in Aspects of Network and information Security , 274-282 (2008), , NATO Advanced Studies Institute on Network Security and Intrusion Detection, IOS Press, Amsterdam

Edge detection algorithm based on DCT continuous extension technique

Asatryan D.G. et Patera J., Edge detection algorithm based on DCT continuous extension technique 71, 795-799 (2008), , Physics of Atomic Nuclei

Image sampling with quasicrystals

Grundland, Mark, Patera, Jiri, Masàkovà, Zuzana et Dodgson, Neil A., Image sampling with quasicrystals 5, Paper 075, 23 (2008), , SIGMA Symmetry Integrability Geom. Methods Appl.

The rings of n-dimensional polytopes

Hàkovà, L., Larouche, M. et Patera, J., The rings of n-dimensional polytopes 41, 495202, 21 (2008), , J. Phys. A

Three-dimensional C-, S- and E-transforms

Nesterenko, Maryna et Patera, Jiri, Three-dimensional C-, S- and E-transforms 41, 475205, 31 (2008), , J. Phys. A

Computing with almost periodic functions

Moody, R. V., Nesterenko, M. et Patera, J., Computing with almost periodic functions 64, 654--669 (2008), , Acta Crystallogr. Sect. A

Alternating multivariate trigonometric functions and corresponding Fourier transforms

Klimyk, A. U. et Patera, J., Alternating multivariate trigonometric functions and corresponding Fourier transforms 41, 145205, 16 (2008), , J. Phys. A

Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements

Boyko, Vyacheslav, Patera, Ji\v rí et Popovych, Roman, Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements 428, 834--854 (2008), , Linear Algebra Appl.

E-orbit functions

Klimyk, Anatoliy U. et Patera, Ji\v rí, E-orbit functions 4, Paper 002, 57 (2008), , SIGMA Symmetry Integrability Geom. Methods Appl.

(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms

Klimyk, A. et Patera, J., (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms 48, 093504, 24 (2007), , J. Math. Phys.

Fine group gradings of the real forms of sl(4,C), sp(4,C), and o(4,C)

Patera, Jiri, Pelantovà, Edita et Svobodovà, Milena, Fine group gradings of the real forms of sl(4,C), sp(4,C), and o(4,C) 48, 093503, 25 (2007), , J. Math. Phys.

Discrete and continuous exponential transforms of simple Lie groups of rank 2

Kashuba, I. et Patera, J., Discrete and continuous exponential transforms of simple Lie groups of rank 2 40, 4751--4774 (2007), , J. Phys. A

Invariants of solvable Lie algebras with one nilindependent diagonal element

Boyko, Vyacheslav, Patera, Ji\v rí et Popovych, Roman, Invariants of solvable Lie algebras with one nilindependent diagonal element 40, (2007), , J. Phys. A

(Anti)symmetric multidimensional exponential functions and the corresponding Fourier transforms

Klimyk, Anatoliy et Patera, Jiri, (Anti)symmetric multidimensional exponential functions and the corresponding Fourier transforms 40, 10473-10489 (2007), , J.Phys.A

Antisymmetric orbit functions

Klimyk A.U. et Patera, J., Antisymmetric orbit functions 3, 83 (2007), , SIGMA (Symmetry,Integrability and Geometry: Methods and Applications)

Invariants of triangular Lie algebras

Boyko V., Patera J. et Popovych R., Invariants of triangular Lie algebras 40, (2007), , J. Phys. A: Math. Theor.

Fine gradings of the real forms of sl(4,C), sp(4,C) and o(4,C)

Patera J., Pelantova E. et Svobodova M., Fine gradings of the real forms of sl(4,C), sp(4,C) and o(4,C) 48, (2007), , J. Math. Phys.

The discrete SU3 transform and its continuous extension for triangular lattices

Atoyan A. et Patera, J., The discrete SU3 transform and its continuous extension for triangular lattices 57, 745-764 (2007), , J. Geom. Physics

Invariants of Lie algebras with fixed structure of nilradicals

Boyko, Vyacheslav, Patera, Jiri et Popovych, Roman, Invariants of Lie algebras with fixed structure of nilradicals 40, 113-130 (2007), , J. Phys. A

Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group

Moody, Robert V. et Patera, Ji\v rí, Orthogonality within the families of C-, S-, and E-functions of any compact semisimple Lie group 2, Paper 076, 14 (2006), , SIGMA Symmetry Integrability Geom. Methods Appl.

Graded contractions of the Pauli graded sl(3,C)

Hrivnàk, J., Novotny, P., Patera, J. et Tolar, J., Graded contractions of the Pauli graded sl(3,C) 418, 498-550 (2006), , Linear Algebra Appl.

Computation of invariants of Lie algebras by means of moving frames

Boyko, Vyacheslav, Patera, Ji\v rí et Popovych, Roman, Computation of invariants of Lie algebras by means of moving frames 39, 5749-5762 (2006), , J. Phys. A

Discrete and continuous sine transform generalized to semisimple Lie groups of rank two

Patera, J. et Zaratsyan, A., Discrete and continuous sine transform generalized to semisimple Lie groups of rank two 47, 043512, 22 (2006), , J. Math. Phys.

Orbit functions

Klimyk, Anatoliy et Patera, Jiri, Orbit functions 2, Paper 006, 60 (2006), , SIGMA Symmetry Integrability Geom. Methods Appl.

Cosine transform generalized to Lie groups SU(2)xSU(2) and O(5): application to textural image processing

M. GERMAIN, J. PATERA, Cosine transform generalized to Lie groups SU(2)xSU(2) and O(5): application to textural image processing , (2006), , Canadian Conference on Electrical and Computer Engineering, IEEE Canada

Multiresolution analysis of digital images using the continuous extension of discrete group transforms

M. GERMAIN, J. PATERA, Multiresolution analysis of digital images using the continuous extension of discrete group transforms , 6-15 (2006), , SPIE 6065, Computational Imaging IV; Charles A. Bouman, Eric L.Miller, Ilya Pollak; Eds

Interpolation using cosine transforms generalized to Lie groups

J. PATERA, A. ZARATSYAN, H. ZHU, Interpolation using cosine transforms generalized to Lie groups , (2006), , SPIE 6064, Image Processing

Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(3) and G(2)

Patera, J. et Zaratsyan, A., Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(3) and G(2) 46, 113506, 17 (2005), , J. Math. Phys.

Compact simple Lie groups and their $C$-, $S$-, and $E$-transforms

Patera, Jiri, Compact simple Lie groups and their $C$-, $S$-, and $E$-transforms 1, Paper 025, 6 (2005), , SIGMA Symmetry Integrability Geom. Methods Appl.

Classification of Voronoi and Delone tiles of quasicrystals. III. Decagonal acceptance window of any size

Masàkovà, Z., Patera, J. et Zich, J., Classification of Voronoi and Delone tiles of quasicrystals. III. Decagonal acceptance window of any size 38, 1947-1960 (2005), , J. Phys. A

Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(2)xSU(2) and O(5)

Patera, J. et Zaratsyan, A., Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(2)xSU(2) and O(5) 46, 113506, 17 (2005), , J. Math. Phys.

Fourier transform method for imaging atmospheric Cherenkov telescopes

Atoyan, A., Patera, J., Sahakian, V., et Akhperjanian, A, Fourier transform method for imaging atmospheric Cherenkov telescopes 23, 79-95 (2005), , Astroparticle Phys.

Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization

Atoyan, A. et Patera, J., Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization 45, 2468-2491 (2004), , J. Math. Phys.

Fine gradings of o(4,C),

Patera, Jiri, Pelantovà, Edita et Svobodovà, Milena, Fine gradings of o(4,C), 45, 2188-2198 (2004), , J. Math. Phys.

Pauli graded contractions of sl(3,C)

M. HAVLICEK, J. PATERA, E. PELANTOVA, Pauli graded contractions of sl(3,C) , 37-42 (2004), , Nonlinear Math. Phys., suppl.,11

Symmetry in Nonlinear Mathematical physics

PATERA J, Symmetry in Nonlinear Mathematical physics , 1152-1160 (2004), , Of the Nat. Acad. Sci, 30

Sharp and generating functions in group theory, in Symmetry in physics

PATERA J., R.T., Sharp and generating functions in group theory, in Symmetry in physics 34, 159-163 (2004), , CRM Proccedings and Lecture Notes

Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals : General Method

Masakovà , Z., Patera, J. et Zich, J., Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals : General Method 36, 1869-1894 (2003), , J. Phys. A

Statistics and implementation of aperiodic pseudorandom number generators

Guimond, Louis-Sébastien, Patera, Jan et Patera, Jiri, Statistics and implementation of aperiodic pseudorandom number generators 46, 295-318 (2003), , Appl. Numer. Math.

Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals with circular acceptance window of arbitrary size

Masàkovà, Z., Patera, J. et Zich, J., Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals with circular acceptance window of arbitrary size 36, 1895-1912 (2003), , J. Phys. A

Graded contractions of Jordan algebras and of their representations

Kashuba, Iryna et Patera, Ji\v rí, Graded contractions of Jordan algebras and of their representations 36, 12453-12473 (2003), , J. Phys. A

Algebraic solutions of the Neumann boundery value problems on fundamental region of a compact semisimple Lie group

PATERA J, Algebraic solutions of the Neumann boundery value problems on fundamental region of a compact semisimple Lie group , 26-31 (2003), , group theory and numerical methods, Montreal

Continuous extension of the discrete cosine transform and its applications to data processing, Proceedings of the Workshop

ATOYAN A, PATERA J, Continuous extension of the discrete cosine transform and its applications to data processing, Proceedings of the Workshop , 26-31 (2003), , Group theory and numerical methods, Montréal

Application of the continuous extension of discrete cosine transform to images taken by FLIR detectors

ATOYAN A, PATERA J, Application of the continuous extension of discrete cosine transform to images taken by FLIR detectors , (2003), , NATO ASI 2003, Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management

Application of multidimensional discrete transforms on Lie groups for image processing

AKHPERJANIAN A., ATOYAN A., PATERA J., SAHAKIAN V., Application of multidimensional discrete transforms on Lie groups for image processing , (2003), , NATO ASI 2003

Innate brain language and grammar: Implications for human language and music, in Stochastic point processes

SHAW G., BODNER M., PATERA J., Innate brain language and grammar: Implications for human language and music, in Stochastic point processes , 287-305 (2003), , Srinivasan and A. Vihayakumar, Narosa Publishing, New Delhi

The eight fine gradings of sl(4,C) and o(6,C)

Patera, Jiri, Pelantovà, Edita et Svobodovà, Milena, The eight fine gradings of sl(4,C) and o(6,C) 43, 6353-6378 (2002), , J. Math. Phys.

Affine extension of noncrystallographic Coxeter groups and quasicrystals

Patera, Jiri et Twarock, Reidun, Affine extension of noncrystallographic Coxeter groups and quasicrystals 35, 1551-1574 (2002), , J. Phys. A

Automorphisms of a finest grading of sl(n,C)

Havlícek, Miloslav, Patera, Jiri, Pelantovà, Edita et Tolar, Jiri, Automorphisms of a finest grading of sl(n,C) 43, 1083-1094 (2002), , J. Math. Phys.

The Music-Math Connection

Bodner M., Derr C., Leng X., Patera J., Petterson M., Ticheli F., Vuong S. et Shaw g., The Music-Math Connection Number 3, 9-16 (2002), , Early Childhood Connections 8

Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals

Guimond, Louis-Sébastien et Patera, Jiri, Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals 71, 319-332 (electronic) (2002), , Math. Comp.

Combining random number generators using cut and project sequences

Guimond, Louis-Sébastien, Patera, Jiri et Patera, Jan, Combining random number generators using cut and project sequences 51, 305--311 (2001), , Czechoslovak J. Phys.

Fine grading of o(5, C), sp(4, C) and of their real forms

Patera, Jiri, Pelantovà, Edita et Svobodovà, Milena, Fine grading of o(5, C), sp(4, C) and of their real forms 42, 3839-3853 (2001), , J. Math. Phys.

On fine gradings and their symmetries

Masakovà A., Patera J., Pelantovà E. et Tolar, J., On fine gradings and their symmetries 51, 383-391 (2001), , Czechoslovak J. Phys.

Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals

Masakovà A., Patera J. et Pelantovà E., Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals 79, 669-687 (2001), , Can. J. Phys. (Gerhard Herzberg memorial issue)

Acceptance windows compatible with a quasicrystal fragment, in From Quasicrystals to More Complex Systems

Masakovà, Zuzana, Patera, Jiri et Pelantovà, Edita, Acceptance windows compatible with a quasicrystal fragment, in From Quasicrystals to More Complex Systems 13, 167-193 (2000), , ed. F. Axel, F. Denoyer, J.P. Gazeau, Springer, Centre de Physique des Houches

On Lie gradings. III. Gradings of the real forms of classical Lie algebras

Havlícek, Miloslav, Patera, Jiri et Pelantovà, Edita, On Lie gradings. III. Gradings of the real forms of classical Lie algebras 314, 1-47 (2000), , Linear Algebra Appl.

sl(3, C) generator matrix elements in a Pauli subgroup basis

de Guise, H., Patera, J. et Sharp, R. T., sl(3, C) generator matrix elements in a Pauli subgroup basis 41, 4860-4880 (2000), , J. Math. Phys.

The fine gradings of sl(3,C) and their symmetries

HAVLICEK M., PATERA J. & PELANTOVA E. ET TOLAR J., The fine gradings of sl(3,C) and their symmetries 1, 57-61 (2000), , Group Theor. Methods in Physics, Eds. A.N. Sissakian, G.S. Pogosyan and L.G. Mardoyan

Lattice-like properties of quasicrystal models with quadratic irrationalities, in Quantum Theory and Symmetries

MASSAKOVA Z., PATERA J. & PELANTOVA E., Lattice-like properties of quasicrystal models with quadratic irrationalities, in Quantum Theory and Symmetries , 499-509 (2000), , H.D. Doebner, V.K.Dobrev, J.-D.Hennig, W. Lucke, Word Scientific

Quasicrystal Lie algebras and their generalizations

Patera, Jiri et Twarock, Reidun, Quasicrystal Lie algebras and their generalizations 315, 241-256 (1999), , Phys. Rep.

Graded contractions of the Lie algebra e(2,1)

Patera, J., Pogosyan, G. et Winternitz, P., Graded contractions of the Lie algebra e(2,1) 32, 805-826 (1999), , J. Phys. A

Non-crystallographic root systems, in Quasicrystals and Discrete Geometry

Chen L., Moody R.V. et Patera J., Non-crystallographic root systems, in Quasicrystals and Discrete Geometry 10, 135-178 (1998), , Fields Institute Monograph Series

Densities, minimal distances, and coverings of quasicrystals

Moody, R. V. et Patera, J., Densities, minimal distances, and coverings of quasicrystals 195, 613-626 (1998), , Comm. Math. Phys.

Minimal distances in quasicrystals

Masàkovà, Z., Patera, J. et Pelantovà, E., Minimal distances in quasicrystals 31, 1539-1552 (1998), , J. Phys. A

Inflation centers in cut and project quasicrystals

Masàkovà, Zuzana, Patera, Jiri et Pelantovà, Edita, Inflation centers in cut and project quasicrystals 31, 1443-1453 (1998), , J. Phys. A

Quasicrystal Lie algebras

Patera, Jiri, Pelantovà, Edita et Twarock, Reidun, Quasicrystal Lie algebras 246, 209-213 (1998), , Phys. Lett. A

Tau wavelets in the plane

Gazeau, Jean Pierre, Patera, Jiri et Pelantovà, Edita, Tau wavelets in the plane 39, 4201-4212 (1998), , J. Math. Phys.

Selfsimilar Delone sets and cut and project quasicrystals

Masàkovà , Zuzana, Patera, Jiri et Pelantovà , Edita, Selfsimilar Delone sets and cut and project quasicrystals 31, 4927-4946 (1998), , J. Phys. A

On Liegradings II

Havlicek, Miloslav, Patera, Jiri et Pelantova, Edita, On Liegradings II 277, 97-125 (1998), , Linear Algebra Appl.

On gradings of Lie algebras and représentations, in Lie Theory and its Applications II

PATERA J. & TOLAR J., On gradings of Lie algebras and représentations, in Lie Theory and its Applications II , 109-118 (1998), , H.-D. Doebner, V.K. Dobrev, and J. Hilgert, World Scientific, Singapore

The signatures of finite dimensional representations of the de Sitter groups SO (4,1) and SO (3,2)

Grimm, S., de Montigny, M. et Patera, J., The signatures of finite dimensional representations of the de Sitter groups SO (4,1) and SO (3,2) 30, 7463-7471 (1997), , J. Phys. A

On the fine gradings of simple classical Lie algebras

Havlicek, Miloslav, Patera, Jiri et Pelantovà, Edita, On the fine gradings of simple classical Lie algebras 12, 189-194 (1997), , Internat. J. Modern Phys. A

Non-crystallographic root systems and quasicrystals, Proc. NATO ASI Aperiodic Long Ranger Order

PATERA, J., Non-crystallographic root systems and quasicrystals, Proc. NATO ASI Aperiodic Long Ranger Order , 443-465 (1997), , Waterloo, Ontario, Canada

Decomposition of tensor products of the fundamental representations of E8, in Advances in Mathematical Sciences

Grimm S. et Patera J., Decomposition of tensor products of the fundamental representations of E8, in Advances in Mathematical Sciences 11, 329-355 (1997), , CRM's 25 Years

Simple physical generation of quasicrystals

Janot C. et Patera J., Simple physical generation of quasicrystals 233, 110-114 (1997), , Phys. Lett. A

Dynamical generation of quasicrystals

Moody, R. V. et Patera, J., Dynamical generation of quasicrystals 36, 291-300 (1996), , Lett. Math. Phys.

Tau-wavelets of Haar

Gazeau, J.-P. et Patera, J., Tau-wavelets of Haar 29, 4549-4559 (1996), , J. Phys. A

Generating functions for the Coxeter group H4

Lam, C. S., Patera, J. et Sharp, R. T., Generating functions for the Coxeter group H4 29, 7705-7719 (1996), , J. Phys. A

Grading refinements in the contractions of Lie algebras and their invariants

Ait Abdelmalek, M., Leng, X., Patera, J. et Winternitz, P., Grading refinements in the contractions of Lie algebras and their invariants 29, 7519-7543 (1996), , J. Phys. A

Graded contractions of representations of orthogonal and symplectic Lie algebras with respect to their maximal parabolic subalgebras

Leng, Xiaodan et Patera, J., Graded contractions of representations of orthogonal and symplectic Lie algebras with respect to their maximal parabolic subalgebras 28, 3785-3807 (1995), , J. Phys. A

Voronoi domains and dual cells in the generalized kaleidoscope with applications to root and weight lattices

Moody, R. V. et Patera, J., Voronoi domains and dual cells in the generalized kaleidoscope with applications to root and weight lattices 47, 573-605 (1995), , Canad. J. Math.

The pentacrystals

PATERA J., The pentacrystals , 17-31 (1995), , Les Editions de Physique, eds. F. Axel and D. Gratias, Springer

Description of reflection generated polytopes using decorated Coxeter diagrams

Champagne B., Kjiri M., Patera J. et Sharp R.T., Description of reflection generated polytopes using decorated Coxeter diagrams 73, 566-584 (1995), , Can. J. Phys.

Colourings of quasicrystals

Moody, R. V. et Patera, J., Colourings of quasicrystals 72, 442-452 (1994), , Canad. J. Phys.

Graded contractions of the affine Lie algebra $A^{(1)}_1$, its representations and tensor products, and an application to the branching rule $A^{(1)}_1\supset A^{(1)}_1$

Hussin, A., King, R. C., Leng, X. et Patera, J., Graded contractions of the affine Lie algebra $A^{(1)}_1$, its representations and tensor products, and an application to the branching rule $A^{(1)}_1\supset A^{(1)}_1$ 27, 4125-4152 (1994), , J. Phys. A

Transitively differential groups of degree three

Kantor, I. L. et Patera, J., Transitively differential groups of degree three 35, 443-458 (1994), , J. Math. Phys.

Graded contractions and kinematical groups of space-time

de Montigny, M., Patera, J. et Tolar, J., Graded contractions and kinematical groups of space-time 35, 405-425 (1994), , J. Math. Phys.

Graded contractions of representations of special linear Lie algebras with respect to their maximal parabolic subalgebras

Leng, Xiaodan et Patera, J., Graded contractions of representations of special linear Lie algebras with respect to their maximal parabolic subalgebras 27, 1233-1250 (1994), , J. Phys. A

Graded contractions of Casimir operators

Bincer, A. M. et Patera, J., Graded contractions of Casimir operators 26, 5621-5628 (1993), , J. Phys. A

Quasicrystals and icosians

Moody, R. V. et Patera, J., Quasicrystals and icosians 26, 2829-2853 (1993), , J. Phys. A

Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams

Moody, R. V. et Patera, J., Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams 25, 5089-5134 (1992), , J. Phys. A

Orbit-orbit branching rules between simple low-rank algebras and equal-rank subalgebras

Gingras, F., Patera, J. et Sharp, R. T., Orbit-orbit branching rules between simple low-rank algebras and equal-rank subalgebras 33, 1618-1626 (1992), , J. Math. Phys.

Discrete and continuous graded contractions of Lie algebras and superalgebras

de Montigny, M. et Patera, J., Discrete and continuous graded contractions of Lie algebras and superalgebras 24, 525-547 (1991), , J. Phys. A

The higher rank Virasoro algebras

Patera, J. et Zassenhaus, H., The higher rank Virasoro algebras 136, 1-14 (1991), , Comm. Math. Phys.

Discrete and continuous graded contractions of representations of Lie algebras

Moody, R. V. et Patera, J., Discrete and continuous graded contractions of representations of Lie algebras 24, 2227-2257 (1991), , J. Phys. A

Affine Kac-Moody Algebras, Weight Multiplicities and Branching Rules

KASS S., MOODY R.V,PATERA J. ET SLANSKY, Affine Kac-Moody Algebras, Weight Multiplicities and Branching Rules 1 & 2, 897 (1991), , University of California Press, Berkeley

Graded contractions of sl(3,C)

Couture, M., Patera, J., Sharp, R. T. et Winternitz, P., Graded contractions of sl(3,C) 32, 2310-2318 (1991), , J. Math. Phys.

Solvable Lie algebras of dimension 4 over perfect fields

Patera, J. et Zassenhaus, H., Solvable Lie algebras of dimension 4 over perfect fields 142, 1-17 (1990), , Linear Algebra Appl.

Simplie Users Manual; Macintosh software for représentations of simple Lie algebras

McKAY W.G., PATERA J. & RAND D., Simplie Users Manual; Macintosh software for représentations of simple Lie algebras , 49 (1990), , Les publicaions CRM, Montréal

Tables of représentations of simple Lie algebras

McKAY W.G., PATERA J. & RAND D., Tables of représentations of simple Lie algebras Exceptional simple Lie algebras, 318 (1990), , Les publications CRM

On intersections of A1 subgroups in the exceptional simple Lie groups E6, E7, E8

Patera, J., Rodri­guez, M. et Zaoui, M., On intersections of A1 subgroups in the exceptional simple Lie groups E6, E7, E8 23, 5695-5705 (1990), , J. Phys. A

Subjoinings of affine Kac-Moody algebras

Leng, X., Patera, J. et Sharp, R. T., Subjoinings of affine Kac-Moody algebras 23, 3397-3407 (1990), , J. Phys. A

The construction of solvable Lie algebras from equidimensional nilpotent algebras

Patera, J. et Zassenhaus, H., The construction of solvable Lie algebras from equidimensional nilpotent algebras 133, 89-120 (1990), , Linear Algebra Appl.

The 785 conjugacy classes of rational elements of finite order in E8

McKay W.G., Moody R.V., Patera J. et Pianzola A., The 785 conjugacy classes of rational elements of finite order in E8 110, 79-123 (1990), , Contemporary Math.

Tables od dominant weight multiplicities for représentations of simple Lie algebras

McKAY W.G., PATERA J. & RAND D., Tables od dominant weight multiplicities for représentations of simple Lie algebras , 340 (1985), , Mercel Dekker, New York

Tables of dimensions, incidences, and branching rules for représentations of simple Lie algebras

McKAY, W.G., PATERA, J., Tables of dimensions, incidences, and branching rules for représentations of simple Lie algebras , 317 (1981), , Marcel Dekker, New Yord

Branching rules for représentations of simple Lie algebras

PATERA, J. SANKOFF, D., Branching rules for représentations of simple Lie algebras , 99 (1973), , Presses Université de Montréal

Prix et distinctions

  • Conseil des arts du Canada Bourse Killam, 1991