Computer physics communications, ISSN 0010-4655, 2015, Volume 192, Issue C, pp. 166 - 195

We present the Mathematica application “LieART” (LieAlgebras and Representation Theory...

Irreducible representation | Model building | Tensor product | GUT | Representation theory | Lie group | Lie algebra | Branching rule | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODEL | PHYSICS, MATHEMATICAL | Algebra | Tensors | Computation | Mathematical analysis | Lie groups | Mathematical models | Labels | Decomposition | Representations

Irreducible representation | Model building | Tensor product | GUT | Representation theory | Lie group | Lie algebra | Branching rule | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODEL | PHYSICS, MATHEMATICAL | Algebra | Tensors | Computation | Mathematical analysis | Lie groups | Mathematical models | Labels | Decomposition | Representations

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 12/2018, Volume 90, Issue 6

We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs...

Higher-rank graphs | Purely atomic representations | Irreducible representations | Permutative representations | Projection-valued measure | ITERATED FUNCTION SYSTEMS | ENDOMORPHISMS | CORRELATED STATES | SEMIGROUP | SPACE | MATHEMATICS | KMS STATES | CUNTZ-KRIEGER ALGEBRAS | WAVELETS

Higher-rank graphs | Purely atomic representations | Irreducible representations | Permutative representations | Projection-valued measure | ITERATED FUNCTION SYSTEMS | ENDOMORPHISMS | CORRELATED STATES | SEMIGROUP | SPACE | MATHEMATICS | KMS STATES | CUNTZ-KRIEGER ALGEBRAS | WAVELETS

Journal Article

Computer physics communications, ISSN 0010-4655, 2012, Volume 183, Issue 11, pp. 2480 - 2493

In this paper we present Affine.m—a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms...

Kac–Moody algebra | Weights | Irreducible modules, CFT, integrable systems | Mathematica | Affine Lie algebra | Lie algebra | Root system | Kac-Moody algebra | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | Mathematics | PHYSICS, MATHEMATICAL | Analysis | Algorithms | Algebra | Computation | Mathematical analysis | Lie groups | Summaries | Representations | Symmetry

Kac–Moody algebra | Weights | Irreducible modules, CFT, integrable systems | Mathematica | Affine Lie algebra | Lie algebra | Root system | Kac-Moody algebra | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | Mathematics | PHYSICS, MATHEMATICAL | Analysis | Algorithms | Algebra | Computation | Mathematical analysis | Lie groups | Summaries | Representations | Symmetry

Journal Article

Journal of algebra, ISSN 0021-8693, 2007, Volume 312, Issue 2, pp. 829 - 848

In this note we present a complete analysis of finite-dimensional representations of the Lie superalgebra sl ( 2 | 1...

Representation theory | Lie superalgebras | DISORDERED-SYSTEMS | LIE SUPER-ALGEBRAS | SUPERSYMMETRY | SPL(2,1) | CLASSIFICATION | SIGMA-MODEL | IRREDUCIBLE REPRESENTATIONS | CHARACTERS | MATHEMATICS | CONFORMAL FIELD-THEORY | representation theory | SUPERALGEBRAS

Representation theory | Lie superalgebras | DISORDERED-SYSTEMS | LIE SUPER-ALGEBRAS | SUPERSYMMETRY | SPL(2,1) | CLASSIFICATION | SIGMA-MODEL | IRREDUCIBLE REPRESENTATIONS | CHARACTERS | MATHEMATICS | CONFORMAL FIELD-THEORY | representation theory | SUPERALGEBRAS

Journal Article

Journal of applied crystallography, ISSN 1600-5767, 2017, Volume 50, Issue 5, pp. 1457 - 1477

.... In the symmetry analysis of such systems, instead of the irreducible representations of the space groups, it is necessary to consider the single- and double-valued irreducible representations of the double space groups...

band representations | double crystallographic groups | computer programs | single‐valued and double‐valued irreducible representations | Bilbao Crystallographic Server | single-valued and double-valued irreducible representations | SPACE-GROUPS | SYMMETRY | ENERGY-BANDS | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | File servers | Analysis | Databases | Diffraction | Brillouin zones | Insulators | Representations | Microstructure | Crystallography | Data bases | Symmetry | Chemistry

band representations | double crystallographic groups | computer programs | single‐valued and double‐valued irreducible representations | Bilbao Crystallographic Server | single-valued and double-valued irreducible representations | SPACE-GROUPS | SYMMETRY | ENERGY-BANDS | CRYSTALLOGRAPHY | CHEMISTRY, MULTIDISCIPLINARY | File servers | Analysis | Databases | Diffraction | Brillouin zones | Insulators | Representations | Microstructure | Crystallography | Data bases | Symmetry | Chemistry

Journal Article

Journal of Algebra, ISSN 0021-8693, 2009, Volume 322, Issue 6, pp. 1877 - 1918

The irreducible components of varieties parametrizing the finite dimensional representations of a finite dimensional algebra Λ...

Representations of finite dimensional algebras | Generic properties of representations | Irreducible components of parameterizing varieties | Path algebras modulo relations | MATHEMATICS | MODULES | SUBREPRESENTATIONS | VARIETIES | UNISERIAL REPRESENTATIONS | FINITE-DIMENSIONAL ALGEBRAS | GEOMETRY

Representations of finite dimensional algebras | Generic properties of representations | Irreducible components of parameterizing varieties | Path algebras modulo relations | MATHEMATICS | MODULES | SUBREPRESENTATIONS | VARIETIES | UNISERIAL REPRESENTATIONS | FINITE-DIMENSIONAL ALGEBRAS | GEOMETRY

Journal Article

Applied Categorical Structures, ISSN 0927-2852, 10/2014, Volume 22, Issue 5, pp. 907 - 929

... Birkhoff in the 1940s to his subdirect representation theorem for general algebras. The Hilbert-Noether-Birkhoff linkage was brought to light in the late 1990s in talks by Bill Lawvere...

Geometry | Residually small category | Convex and Discrete Geometry | HNB category | Subdirect representation | Mathematics | Theory of Computation | Nullstellensatz | Subdirectly irreducible object | Mathematical Logic and Foundations | MATHEMATICS | CATEGORIES | Analysis | Algebra

Geometry | Residually small category | Convex and Discrete Geometry | HNB category | Subdirect representation | Mathematics | Theory of Computation | Nullstellensatz | Subdirectly irreducible object | Mathematical Logic and Foundations | MATHEMATICS | CATEGORIES | Analysis | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2015, Volume 18, Issue 2, pp. 477 - 490

In this paper we prove that every irredicuble representation of a Leibniz algebra can be obtained from irreducible representations of the semisimple Lie algebra from the Levi decomposition...

Primary 17A32 | Associative Rings and Algebras | Irreducible representation | Non-associative Rings and Algebras | Semisimple algebra | Secondary 17B10 | Commutative Rings and Algebras | Leibniz algebra | Mathematics | Representation | MATHEMATICS | Algebra

Primary 17A32 | Associative Rings and Algebras | Irreducible representation | Non-associative Rings and Algebras | Semisimple algebra | Secondary 17B10 | Commutative Rings and Algebras | Leibniz algebra | Mathematics | Representation | MATHEMATICS | Algebra

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 03/2016, Volume 57, Issue 3, p. 31701

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula...

PHYSICS, MATHEMATICAL | GAUGE-THEORIES | GROWTH | Yang-Mills theory | Recall | Representations | Mathematics | Mathematical Physics | High Energy Physics - Theory | Representation Theory | Physics | TOPOLOGY | YANG-MILLS THEORY | TWO-DIMENSIONAL CALCULATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IRREDUCIBLE REPRESENTATIONS

PHYSICS, MATHEMATICAL | GAUGE-THEORIES | GROWTH | Yang-Mills theory | Recall | Representations | Mathematics | Mathematical Physics | High Energy Physics - Theory | Representation Theory | Physics | TOPOLOGY | YANG-MILLS THEORY | TWO-DIMENSIONAL CALCULATIONS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | IRREDUCIBLE REPRESENTATIONS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 07/2017, Volume 58, Issue 7, p. 71705

...-invariant systems in terms of strongly continuous irreducible unitary representations (IRS) of B. Here we introduce the analogue B...

GROUP THEORETICAL APPROACH | UNITARY REPRESENTATIONS | GENERAL-RELATIVITY | ASYMPTOTIC SYMMETRIES | GRAVITATIONAL WAVES | CONSTRUCTION | CANONICAL QUANTIZATION | BMS GROUP | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS | GRAVITY | Supersymmetry | Topology | Representations | Relativity | Symmetry

GROUP THEORETICAL APPROACH | UNITARY REPRESENTATIONS | GENERAL-RELATIVITY | ASYMPTOTIC SYMMETRIES | GRAVITATIONAL WAVES | CONSTRUCTION | CANONICAL QUANTIZATION | BMS GROUP | PHYSICS, MATHEMATICAL | IRREDUCIBLE REPRESENTATIONS | GRAVITY | Supersymmetry | Topology | Representations | Relativity | Symmetry

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 06/2020, Volume 373, Issue 6, pp. 4223 - 4253

Inspired by the Gan-Gross-Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent representations of unitary groups over finite fields...

MATHEMATICS | LOCAL ROOT NUMBERS | CRITICAL L-VALUES | RESTRICTION PROBLEMS | WEIL REPRESENTATIONS | ORTHOGONAL GROUPS | GROSS-PRASAD CONJECTURE | REDUCTIVE GROUPS | IRREDUCIBLE REPRESENTATIONS

MATHEMATICS | LOCAL ROOT NUMBERS | CRITICAL L-VALUES | RESTRICTION PROBLEMS | WEIL REPRESENTATIONS | ORTHOGONAL GROUPS | GROSS-PRASAD CONJECTURE | REDUCTIVE GROUPS | IRREDUCIBLE REPRESENTATIONS

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 01/2018, Volume 17, Issue 1

Necessary and sufficient conditions for a group to possess a faithful irreducible representation are investigated...

locally finite group | irreducible representation | Faithful representation | locally cyclic group | MATHEMATICS | MATHEMATICS, APPLIED

locally finite group | irreducible representation | Faithful representation | locally cyclic group | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

13.
Full Text
Unitary irreducible representations of SL (2,C) in discrete and continuous SU (1,1) bases

Journal of mathematical physics, ISSN 1089-7658, 2011, Volume 52, Issue 1, p. 012501

We derive the matrix elements of generators of unitary irreducible representations of SL(2, C...

COMPLEX ANGULAR MOMENTA | PHYSICS, MATHEMATICAL | QUANTUM-GRAVITY | HOMOGENEOUS LORENTZ GROUP | Physics - General Relativity and Quantum Cosmology | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | LIE GROUPS | SYMMETRY GROUPS | MATRIX ELEMENTS | SL GROUPS | FUNCTIONS | IRREDUCIBLE REPRESENTATIONS | MATHEMATICAL METHODS AND COMPUTING | SU-2 GROUPS | SU GROUPS | UNITARY SYMMETRY

COMPLEX ANGULAR MOMENTA | PHYSICS, MATHEMATICAL | QUANTUM-GRAVITY | HOMOGENEOUS LORENTZ GROUP | Physics - General Relativity and Quantum Cosmology | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | LIE GROUPS | SYMMETRY GROUPS | MATRIX ELEMENTS | SL GROUPS | FUNCTIONS | IRREDUCIBLE REPRESENTATIONS | MATHEMATICAL METHODS AND COMPUTING | SU-2 GROUPS | SU GROUPS | UNITARY SYMMETRY

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 12/2019, Volume 371, Issue 12, pp. 8699 - 8731

In 2004 the second and third authors introduced a large family of representations of a free group...

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2014, Volume 42, Issue 8, pp. 3507 - 3540

... ). A complete description of irreducible components of the representation variety mod(R, n) is obtained for any dimension n, it is shown that the representation variety is equidimensional...

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | 16G60 | MATHEMATICS | VARIETIES | Primary 16G30 | 16D25 | Algebra | Representations | Planes | Intersections | Modules

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | 16G60 | MATHEMATICS | VARIETIES | Primary 16G30 | 16D25 | Algebra | Representations | Planes | Intersections | Modules

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2017, Volume 489, pp. 179 - 240

Starting with a highest weight representation of a Kac–Moody group over the complex numbers, we construct a monoid whose unit group is the image of the Kac...

Reductive algebraic monoid | Infinite-dimensional algebraic monoid | Kac–Moody group | Weyl group orbit | [formula omitted]-irreducible | J-irreducible | RENNER MONOIDS | MATHEMATICS | ORTHOGONAL ALGEBRAIC MONOIDS | Kac-Moody group | CROSS-SECTION LATTICES | Information science

Reductive algebraic monoid | Infinite-dimensional algebraic monoid | Kac–Moody group | Weyl group orbit | [formula omitted]-irreducible | J-irreducible | RENNER MONOIDS | MATHEMATICS | ORTHOGONAL ALGEBRAIC MONOIDS | Kac-Moody group | CROSS-SECTION LATTICES | Information science

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2014, Volume 278, Issue 3, pp. 663 - 703

We study the quantum affine superalgebra $$U_q(\mathcal {L}\mathfrak {sl}(M,N))$$ U q ( L sl ( M , N ) ) and its finite-dimensional representations...

Mathematics, general | Mathematics | MATHEMATICS | ALGEBRAS | BASES | MODULES | LIE-SUPERALGEBRAS | FINITE-DIMENSIONAL REPRESENTATIONS | UNIVERSAL R-MATRIX | IRREDUCIBLE REPRESENTATIONS | SUPERGROUP UQ(GL(M/N)) | GENERIC-Q

Mathematics, general | Mathematics | MATHEMATICS | ALGEBRAS | BASES | MODULES | LIE-SUPERALGEBRAS | FINITE-DIMENSIONAL REPRESENTATIONS | UNIVERSAL R-MATRIX | IRREDUCIBLE REPRESENTATIONS | SUPERGROUP UQ(GL(M/N)) | GENERIC-Q

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2015, Volume 367, Issue 7, pp. 5059 - 5079

We give precise conditions under which irreducible representations associated to stability groups induce to irreducible representations for Fell bundle C...

Fell bundle C-algebra | Irreducible representation | Ideal structure | Fell bundle | MATHEMATICS | ideal structure | EQUIVALENCE THEOREM | irreducible representation | PRIMITIVE-IDEALS | PRODUCTS

Fell bundle C-algebra | Irreducible representation | Ideal structure | Fell bundle | MATHEMATICS | ideal structure | EQUIVALENCE THEOREM | irreducible representation | PRIMITIVE-IDEALS | PRODUCTS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2019, Volume 371, Issue 8, pp. 5309 - 5340

...} be the nonlinear double cover of G. We discuss a set of small genuine irreducible representations of \widetilde {G...

VARIETY | MATHEMATICS | UNITARY REPRESENTATIONS | MINIMAL REPRESENTATIONS | ALGEBRA | O(P | SEMISIMPLE LIE-GROUPS | IRREDUCIBLE CHARACTERS

VARIETY | MATHEMATICS | UNITARY REPRESENTATIONS | MINIMAL REPRESENTATIONS | ALGEBRA | O(P | SEMISIMPLE LIE-GROUPS | IRREDUCIBLE CHARACTERS

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 2018, Volume 50, Issue 3, p. 281

That the number of irreducible representations of the special unitary group SU(N) SU ( N ) on V.sup. k V a k (which is also the number of Young tableaux with k boxes...

Counting irreducible representations | Representation theory | Special unitary group | Tableaux | Group theory | Computer programming | Algebra | Mathematics - Representation Theory

Counting irreducible representations | Representation theory | Special unitary group | Tableaux | Group theory | Computer programming | Algebra | Mathematics - Representation Theory

Journal Article

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