Jiří Patera

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Jiří Patera is affiliated with the following schools: Université de Montréal, Charles University, Moscow State University

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Why Is Jiří Patera Influential?

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According to Wikipedia, Jiří Patera was a Czech-born Canadian mathematician and academic. He taught at the Université de Montréal and was known for his work in group theory, Lie groups, and cryptography. Life and career Patera attended secondary school in Děčín and subsequently studied theoretical physics at Moscow State University. There he met and married Tatiana Chalnikova. In 1964, he earned a doctorate from Charles University, pursued a postdoc at the University of Montreal and returned to Prague in 1966. In August of 1968, with Soviet tanks rolling into Czechoslovakia, he emigrated with Tatiana and their daughter first to the UK and finally settling in Montreal, Canada, a year later. He joined the Universite de Montreal as an assistant professor and then newly created Centre de Recherches Mathematiques at the university.

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Jiří Patera 's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Invariants of real low dimension Lie algebras (1976) (468)
Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras (1981) (354)
Subalgebras of real three‐ and four‐dimensional Lie algebras (1977) (281)
Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group (1975) (197)
Everything you always wanted to know about SU(3) ⊃ 0(3) (1975) (166)
Quasicrystals and icosians (1993) (145)
Continuous subgroups of the fundamental groups of physics. II. The similitude group (1975) (128)
Discrete and continuous graded contractions of Lie algebras and superalgebras (1991) (127)
Tables of dominant weight mutliplicities for represen-tations of simple Lie algebras (1985) (123)
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3) (1974) (114)
The Pauli matrices in n dimensions and finest gradings of simple Lie algebras (1988) (103)
Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups (1977) (95)
On Lie gradings II (1998) (93)
Discrete and continuous graded contractions of representations of Lie algebras (1991) (93)
Normal forms of elements of classical real and complex Lie and Jordan algebras (1983) (88)
Affine Lie algebras, weight multiplicities, and branching rules (1990) (79)
Subgroups of the Poincaré group and their invariants (1976) (77)
Characters of Elements of Finite Order in Lie Groups (1984) (75)
Quasicrystals and Discrete Geometry (1998) (73)
Tables of branching rules for representations of simple Lie algebras (1973) (71)
Polynomial irreducible tensors for point groups (1978) (70)
The higher rank Virasoro algebras (1991) (67)
Fast recursion formula for weight multiplicities (1982) (63)
Non-crystallographic root systems (1998) (62)
Chiral two-loop-finite supersymmetric theories (1984) (61)
Quantum numbers for particles in de Sitter space (1976) (60)
Antisymmetric Orbit Functions (2007) (60)
E-Orbit Functions (2008) (57)
Computation of Invariants of Lie Algebras by Means of Moving Frames (2006) (52)
Orbit Functions (2006) (50)
On discretization of tori of compact simple Lie groups (2009) (50)
Subgroups of the Euclidean group and symmetry breaking in nonrelativistic quantum mechanics (1977) (50)
Affine extension of noncrystallographic Coxeter groups and quasicrystals (2002) (50)
General indices of representations and Casimir invariants (1984) (47)
Solvable Lie algebras of dimension ⩽4 over perfect fields (1990) (46)
Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagrams (1992) (45)
Subgroups of Lie groups and separation of variables (1981) (45)
Computation of character decompositions of class functions on compact semisimple Lie groups (1987) (44)
Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group (2006) (44)
On Lie gradings III. Gradings of the real forms of classical Lie algebras (2000) (42)
Congruence number, a generalization of SU(3) triality (1980) (42)
Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups (2010) (40)
Higher indices of group representations (1976) (38)
Colourings of quasicrystals (1994) (37)
Description of reflection-generated polytopes using decorated Coxeter diagrams (1995) (37)
Graded contractions and kinematical groups of space–time (1994) (37)
The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1) (1974) (36)
Gaussian Cubature Arising from Hybrid Characters of Simple Lie Groups (2012) (34)
Graded contractions of sl(3,C) (1991) (34)
Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight Lattices (1995) (32)
Noncrystallographic Root Systems and Quasicrystals (1997) (31)
Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms (2007) (31)
On E-discretization of tori of compact simple Lie groups (2009) (30)
Generating functions for plethysms of finite and continuous groups (1980) (30)
Formal analytic continuation of Gel’fand’s finite dimensional representations of gl(n,C) (1979) (30)
Inflation centres of the cut and project quasicrystals (1998) (30)
Decomposition of tensor products of the fundamental representations of (1997) (29)
Discrete and continuous cosine transform generalized to Lie groups SU(3) and G(2) (2005) (29)
On discretization of tori of compact simple Lie groups: II (2012) (29)
Maximal abelian subalgebras of real and complex symplectic Lie algebras (1983) (28)
On a new relation between semisimple Lie algebras (1980) (28)
Embedding of a Simple Lie Group into a Simple Lie Group and Branching Rules (1967) (28)
Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization (2003) (27)
Canonical transformation and accidental degeneracy. III. A unified approach to the problem (1975) (27)
General indices of simple Lie algebras and symmetrized product representations (1983) (26)
Branching rules for representations of simple Lie algebras through Weyl group orbit reduction (1989) (26)
(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms (2007) (25)
The maximal solvable subgroups of SO(p,q) groups (1974) (25)
Orthogonal Polynomials of Compact Simple Lie Groups (2010) (24)
On the Triangle Anomaly Number of SU($N$) Representations (1981) (23)
MINIMAL DISTANCES IN QUASICRYSTALS (1998) (23)
THE COMPUTATION OF BRANCHING RULES FOR REPRESENTATIONS OF SEMISIMPLE LIE ALGEBRAS (1977) (23)
Graded contractions of the Pauli graded sl(3, C) (2005) (23)
Character generators for elements of finite order in simple Lie groups A1, A2, A3, B2, and G2 (1983) (22)
Classification of Finite‐Dimensional Irreducible Representations of Connected Complex Semisimple Lie Groups (1970) (21)
Verma bases for representations of classical simple Lie algebras (1986) (21)
Cubature Formulas of Multivariate Polynomials Arising from Symmetric Orbit Functions (2015) (21)
Generating functions for characters of group representations and their applications (1979) (21)
General charge conjugation operators in simple Lie groups (1984) (21)
Tau-wavelets of Haar (1996) (21)
Invariants of Lie algebras with fixed structure of nilradicals (2006) (20)
Invariants of solvable lie algebras with triangular nilradicals and diagonal nilindependent elements (2007) (20)
DISCRETE AND CONTINUOUS COSINE TRANSFORM GENERALIZED TO LIE GROUPS SU(2)× SU(2) AND O(5) (2005) (20)
Classification of Voronoi and Delone tiles of quasicrystals: III. Decagonal acceptance window of any size (2005) (20)
Orthogonal polynomials of compact simple Lie groups: branching rules for polynomials (2010) (19)
Discrete and continuous sine transform generalized to semisimple Lie groups of rank two (2006) (19)
Computing with almost periodic functions. (2008) (18)
The eight fine gradings of sl(4, C) and o(6, C) (2002) (18)
Subgroups of the similitude group of three-dimensional Minkowski space (1976) (18)
Erratum: Higher indices of group representations (1977) (18)
Grading refinements in the contractions of Lie algebras and their invariants (1996) (17)
Compact Simple Lie Groups and Their C-, S-, and E-Transforms (2005) (17)
Second and fourth indices of plethysms (1981) (17)
Polynomial icosahedral invariants (1988) (17)
Fourier transform method for imaging atmospheric Cherenkov telescopes (2004) (17)
Substitution rules for aperiodic sequences of the cut and project type (2000) (16)
Quasicrystal Lie algebras (1998) (16)
Fine gradings of o(4,C) (2004) (16)
Orbit–orbit branching rules between simple low‐rank algebras and equal‐rank subalgebras (1992) (16)
Self-similar Delone sets and quasicrystals (1998) (15)
The rings of n-dimensional polytopes (2008) (15)
The four sets of additive quantum numbers of SU(3) (1989) (15)
C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60. (2013) (14)
The Demazure–Tits subgroup of a simple Lie group (1988) (13)
Classification of Voronoi and Delone tiles in quasicrystals: I. General method (2003) (13)
Graded contractions of the Lie algebra e(2, 1) (1999) (13)
Dynamical generation of quasicrystals (1996) (13)
Breaking of Icosahedral Symmetry: C 60 to C 70 (2014) (12)
Orbit Functions of Compact Semisimple Lie Groups as Special Functions (2004) (12)
Alternating group and multivariate exponential functions (2009) (11)
Clebsch–Gordan coefficients for E6 and SO(10) unification models (1984) (11)
The construction of solvable lie algebras from equidimensional nilpotent algebras (1990) (11)
Branching rules for the Weyl group orbits of the Lie algebra An (2009) (11)
Labeling States and Constructing Matrix Representations of F4 (1970) (10)
Fine gradings of o(5, C), sp(4, C) and of their real forms (2001) (10)
New families of Weyl group orbit functions (2012) (10)
Six types of E-functions of the Lie groups O(5) and G(2) (2012) (10)
Exceptional simple Lie algebras (1990) (10)
On finite and continuous little groups of representations of semi-simple Lie groups (1982) (10)
Generalized SU(2) spherical harmonics (1982) (10)
Graded contractions of representations of orthogonal and symplectic Lie algebras with respect to their maximal parabolic subalgebras (1995) (9)
Discrete and continuous exponential transforms of simple Lie groups of rank 2 (2007) (9)
Densities, Minimal Distances, and Coverings of Quasicrystals (1998) (9)
Two-Variable Galilei-Group Expansions of Nonrelativistic Scattering Amplitudes (1973) (9)
Discrete and continuous exponential transforms of simple Lie groups of rank two (2007) (9)
Generating functions for SU(2) plethysms with fixed exchange symmetry (1981) (9)
Graded contractions of Casimir operators (1993) (9)
Graded contractions of Jordan algebras and of their representations (2003) (9)
Analytic SU(3) states in a finite subgroup basis (1982) (9)
Continuous extension of the discrete cosine transform, and its applications to data processing (2005) (9)
Graded contractions of Lie algebras, representations and tensor products (2008) (9)
Orbit functions of SU(n) and Chebyshev polynomials (2009) (8)
Alternating multivariate trigonometric functions and corresponding Fourier transforms (2008) (8)
Graded contractions of representations of special linear Lie algebras with respect to their maximal parabolic subalgebras (1994) (8)
Complex orthogonal and symplectic matrices depending on parameters (1982) (8)
Versal deformations of elements of real classical Lie algebras (1982) (8)
Versal deformations of elements of classical Jordan algebras (1983) (8)
1 Prolongation structures of nonlinear evolution equations 8 Singularities for fluids with p = w equation of state 11 Analytic vector harmonic expansions on SU (2) and S2 (1975) (7)
Tau-wavelets in the plane (1998) (7)
Icosahedral symmetry breaking: C60to C84, C108and to related nanotubes (2014) (7)
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes. (2015) (7)
Four families of orthogonal polynomials of C2 and symmetric and antisymmetric generalizations of sine and cosine functions (2011) (7)
Invariants of triangular Lie algebras (2007) (7)
Three-dimensional C-, S- and E-transforms (2008) (7)
Branching rules for Weyl group orbits of simple Lie algebras Bn, Cn and Dn (2011) (7)
Branching rules and Clebsch–Gordan series for E8 (1976) (7)
Affine reflection groups for tiling applications: Knot theory and DNA (2012) (6)
Compact simple Lie groups and their -, -, and -transforms. (2005) (6)
New gradings of sl(3,C) representations (1989) (6)
Invariants of triangular Lie algebras with one nil-independent diagonal element (2007) (6)
Graded contractions of the affine Lie algebra A1(1), its representations and tensor products, and an application to the branching rule A1(1) contains/implies A1(1) (1994) (6)
Elementary Particle Reactions and the Lorentz and Galilei Groups (1975) (5)
A construction of transitively differential groups of degree 3 (1994) (5)
Multiresolution analysis of digital images using the continuous extension of discrete group transforms (2006) (5)
SU(3) × SU(2) × U(1) content of all SU(5) representations (1982) (5)
Congruence classes of finite representations of simple Lie superalgebra (1982) (5)
Simple physical generation of quasicrystals (1997) (5)
Decomposition matrices for the special case of data on the triangular lattice of SU(3) (2017) (5)
Some relations between coupling constants in higher symmetries (1966) (5)
SIGNATURES OF FINITE SU(p,q) REPRESENTATIONS (1984) (5)
Statistical properties and implementation of aperiodic pseudorandom number generators (2003) (5)
Quasicrystal Lie algebras and their generalizations (1999) (5)
Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals (2002) (5)
Combining random number generators using cut and project sequences (2001) (5)
Generating Functions for Orthogonal Polynomials of A2, C2 and G2 (2018) (5)
Classification of Voronoi and Delone tiles of quasicrystals: II. Circular acceptance window of arbitrary size (2003) (5)
Distinguished Bases of sl(n,C) and Their Symmetries (2002) (5)
Clebsch–Gordan coefficients for SU(5)⊇SU(3)×SU(2)×U(1) theories (1983) (5)
The fine gradings of sl(3,C) and their symmetries 1 (2004) (5)
Cosine Transform Generalized to Lie Groups SU(2)XSU(2) AND O(5): Application to Textural Image Processing (2006) (5)
Cosine transform generalized to lie groups SU(2)xSU(2), O(5), and SU(2)xSU(2)xSU(2): application to digital image processing (2006) (5)
Optimal Complete and Optimal Sufficient Sets of Experiments for Elastic Nucleon-Nucleon Scattering (1978) (4)
Three-variable exponential functions of the alternating group (2012) (4)
Angular-momentum basis for a generaljn configuration (1972) (4)
Quadratic irrationalities and geometric properties of one-dimensional quasicrystals (1998) (4)
Polytope contractions within icosahedral symmetry (2014) (4)
CLEBSCH-GORDAN COEFFICIENTS FOR SU(5) UNIFICATION MODELS (1987) (4)
The discrete SU(3) transform and its continuous extension for triangular lattices (2007) (4)
Discrete Two Variable Expansions of Physical Scattering Amplitudes (1976) (4)
Reduction of orbits of finite Coxeter groups of non-crystallographic type (2018) (4)
Finite subgroups of the generalized Lorentz groups O(p,q) (1980) (4)
Polytopes vibrations within Coxeter group symmetries (2016) (4)
On Pauli graded contractions of sl(3, ℂ) (2004) (4)
Image Sampling with Quasicrystals (2009) (4)
The E8 Family of Quasicrystals (1994) (3)
Lattice-like properties of quasicrystal models with quadratic irrationalities (2000) (3)
Dimensions of orbits and strata in complex and real classical Lie algebras (1982) (3)
E‐Discretization of Tori of Exceptional Compact Simple Lie Groups (2009) (3)
A mass formula for resonances with identical strangeness, parity, ordinary and isotopic spin (1972) (3)
SL(3,C) generator matrix elements in a Pauli subgroup basis (2000) (3)
Index of representation of a simple lie algebra (1968) (3)
Generating Function Techniques Pertinent to Spectroscopy and Crystal Physics (1979) (3)
Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals (2001) (3)
On E-functions of semisimple Lie groups (2011) (3)
On the Fine Gradings of Simple Classical Lie Algebras (1997) (3)
Signatures of all finite representations of su (p, q), p + q < = 4 * (1982) (3)
Invariants of Lie algebras via moving frames (2009) (2)
Generating functions for the Coxeter group (1996) (2)
Central Splitting of A2 Discrete Fourier-Weyl Transforms (2020) (2)
GENERATING THE FIBONACCI CHAIN IN O ( log n ) SPACE AND O ( n ) TIME (2003) (2)
Subjoinings of affine Kac-Moody algebras (1990) (2)
The maximal Abelian subgroups of the conformal group of space-time (1978) (2)
Symmetry in Physics (2004) (2)
Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials (2017) (2)
Finite Subgroups of the Lorentz Group and their Generating Functions (1980) (2)
Simple physical generation of aperiodic structures (1998) (2)
Isotopic spin conservation and charge distribution in multipion production (1974) (2)
Indices of representations of simple superalgebras (1987) (2)
R. T. Sharp and generating functions in group theory (2004) (2)
Finite subgroup bases for compact Lie groups (1982) (2)
Highly restricted partitions and angular-momentum states of equivalent particle configurations (1971) (2)
Mass spectra in SU(5) supersymmetric models of grand unification with Higgs particles in representations 75 or 24 (1983) (2)
Quasicrystal Models in Cryptography (2009) (2)
Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations (2011) (2)
Minimal Set of Independent Recursion Relations for SU(2) Clebsch–Gordan Coefficients (1971) (1)
Eigenstates and eigenvalues of labelling operators for O(3) basess of U(3) representations (1984) (1)
Potential Scattering and Galilei-Invariant Expansions of Scattering Amplitudes (1973) (1)
Decomposition matrices for the special case of data on the triangular lattice of G (2) (2018) (1)
Algebraic Methods in Physics : A Symposium for the 60th Birthdays of Jiří Patera and Pavel Winternitz (2001) (1)
Acceptance Windows Compatible with a Quasicrystal Fragment (2000) (1)
Orbit-orbit branching rules (1993) (1)
Fusion of SAR and Multispectral Satellite Images Using Multiscale Analysis and Dempster-Shafer Theory for Flood Extent Extraction (2019) (1)
SU ( n ) Symmetry of Trilinear Interactions (1965) (1)
Statistics and implementation of APRNGs (2000) (1)
Casimir operators of subalgebras of the Poincare Lie algebra and of real Lie algebras of low dimension (1976) (1)
Decomposition matrices for the square lattices of the Lie groups SU(2)×SU(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docum (2019) (1)
Discrete group transforms on SU(2) X SU(2) and SU(3) (2004) (1)
Combining Random Number Generators using Quasicrystals (2000) (1)
Random walk and SU(2) Clebsch–Gordon coefficients (1979) (1)
Group theoretical methods to construct the graphene (2016) (1)
481 Geometric quantization and UIR's of semisimple Lie groups. II. Discrete series 484 Geometric quantization and UIR's of semisimple Lie groups. III. Principal and supplementary series (1982) (0)
Nested Polyhedra and Indices of Orbits of Coxeter Groups of Non-Crystallographic Type (2020) (0)
Discretization of compact semisimple Lie groups (2008) (0)
A pr 2 00 7 Invariants of Triangular Lie Algebras (2008) (0)
Decomposition matrices for the square lattices of the Lie groups $$SU(2)\times SU(2)$$SU(2)×SU(2) (2019) (0)
New families of cryptographic systems (2007) (0)
Dominant Weight Multiplicities in Hybrid Characters of Bn, Cn, F4, G2 (2014) (0)
Internal and external quasicrystal inflation center and their scaling factors (1998) (0)
On Deterministic Replay (2004) (0)
On Distributed Systems Debugging (2004) (0)
Representation theory of compact groups (1980) (0)
Distributed Systems Debugging – State of the Art (2004) (0)
Incompatibility of gauge invariance and nonrelativistic locality in path integral formulation (1972) (0)
BRANCHING RULES FOR SOME REPRESENTATIONS OF THE GROUP SU . (1967) (0)
Selecting Tests (2020) (0)
Symmetries and Integrability of Difference Equations: Lattices of Compact Semisimple Lie Groups (2011) (0)
Se p 20 07 Invariants of Triangular Lie Algebras (2018) (0)
THE SHMUSHKEVICH METHOD FOR HIGHER SYMMETRY GROUPS OF INTERACTING PARTICLES (2013) (0)
The signatures of finite dimensional representations of the de Sitter groups SO and SO (1997) (0)
Polytopes vibrations within Coxeter group symmetries (2016) (0)
Discrete Orthogonality of Bivariate Polynomials of A2, C2 and G2 (2019) (0)
Deterministically broken Periodicity of Linear Congruential Generators using QuasiCrystals (1999) (0)
Asymmetric harmonic oscillator (2022) (0)
Interpolation using cosine transforms generalized to Lie groups (2006) (0)
Ju n 20 07 Invariants of Triangular Lie Algebras (2008) (0)
On the intersections of A1 subgroups in the exceptional simple Lie groups E6, E7 and E8 (1990) (0)
Dimensions, Indices and Congruence Classes of Representations of Affine Kac-Moody Algebras (with examples for affine E8) (1987) (0)
Gaussian Cubature Arising from Hybrid Characters of Simple Lie Groups (2014) (0)
THEORETICAL METHODS TO CONSTRUCT THE GRAPHENE (0)

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