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Representation theory

Definitions and resources

ScienceWISE definitions	External resources
	Representation theory by Internet Encyclopedia of Science Representation theory by Wikipedia

Subcategories and concepts

Subcategories

Concepts

Poisson ring Cellular algebra Absolutely irreducible Admissible representation Affine Hecke algebra Algebra representation Arthur conjectures Association scheme Auslander algebra Auslander-Reiten theory Birman-Wenzl algebra Bose-Mesner algebra Brauer algebra Burau representation Cartan matrix Clifford module Clifford theory Dade isometry Deligne-Lusztig theory Dominance order Equivariant map Exceptional character Faithful representation Freudenthal magic square Fundamental representation Gabriel's theorem Group representation Haagerup property Hecke algebra Highest weight category Hopf algebra Invariant subspace Jucys-Murphy element Kirillov model Kostant partition function Lawrence-Krammer representation Littelmann path model Littlewood-Richardson rule Zoghman Mebkhout Minuscule representation N!-conjecture Opposite group Parabolic induction Plancherel measure Prehomogeneous vector space Quaternionic representation Real representation Reductive dual pair Representation theory of Hopf algebras Restricted representation Riemann-Hilbert correspondence Ringel-Hall algebra Root datum Schubert variety Schur algebra Schur functor Schur-Weyl duality Symplectic representation The Classical Groups Tilting theory Triple system Trivial representation Universal enveloping algebra Vertex of a representation Whittaker model Young's lattice Zuckerman functor Quasiregular element Ring theory Additive identity Algebra homomorphism Arithmetical ring Artin algebra Artinian ideal Artinian ring Artin-Rees lemma Artin-Wedderburn theorem Artin-Zorn theorem Ascending chain condition on principal ideals Azumaya algebra Baer ring Bézout domain Biquaternion Boolean ring Brauer group Brauer-Cartan-Hua theorem C-semiring Category of rings Central simple algebra Classification of Clifford algebras Clifford algebra Coherent ring Commutative ring Composition algebra Composition ring Connected ring Dedekind-Hasse norm Depth of noncommutative subrings Division algebra Division ring Euclidean domain Finite ring Flat map Formal power series Free algebra Free ideal ring GCD domain Geometric algebra Goldie's theorem Goldman domain Graded algebra Hereditary ring Hopkins-Levitzki theorem Integral domain Inversive ring geometry Irreducible element Irreducible ideal Irreducible ring Jacobson density theorem Jacobson ring Jaffard ring Kaplansky's conjecture Köthe conjecture Krull ring Kummer ring Kurosh problem Laurent polynomial Levitzky's theorem Local ring Localization of a ring Loewy ring Matrix ring Modular representation theory Monoid ring Morita equivalence Nakayama algebra Nilpotent Noetherian ring Noncommutative ring Noncommutative unique factorization domain Numerical polynomial Opposite ring Ore condition Ore extension Overring Partially-ordered ring Perfect field Perfect ring Polynomial identity ring Polynomial ring Prime element Prime ring Primitive ring Principal ideal domain Principal ideal ring Product of rings Quotient ring Radical of a ring Real closed ring Idealizer Reduced ring Regular ideal Regular local ring Regular ring Ring extension Ring homomorphism Ring of integers Pseudo-ring Schreier domain Semi-local ring Semifir Semiperfect ring Semiprime ring Semiring Semisimple module Serial module Simple algebra Simple ring Skolem-Noether theorem Square-free Stably finite ring Subring Subring test Symmetric algebra Quasisymmetric function Topological ring Total quotient ring Triangular matrix ring Trivial ring Unipotent Unique factorization domain Unit ring Valuation ring Von Neumann regular ring Wedderburn's little theorem Weyl algebra Witt vector Zero divisor Zero ring Zero-product property Zorn ring B-admissible representation Burnside ring Character theory Commutation theorem Complementary series representation Complex conjugate representation Complex representation Decomposition matrix Dual representation Frobenius-Schur indicator G-module Group action K-finite Molien series Monomial representation Multiplicity-one theorem P-adic Hodge theory Partial group algebra Positive definite function on a group Regular representation Representation rigid group Representation ring Schur orthogonality relations Springer correspondence Brauer's theorem on induced characters Brauer's three main theorems Brauer-Nesbitt theorem Maschke's theorem Principal indecomposable module Robinson-Schensted correspondence Schur polynomial Segal conjecture Specht module Young symmetrizer Young tableau Cuspidal representation Grosshans subgroup Haboush's theorem Lie-Kolchin theorem Rational representation Reductive group Steinberg representation Gårding domain Kazhdan's property Mautner's lemma Principal series representation Quasiregular representation Representative function System of imprimitivity Adjoint endomorphism Affine action Dynkin index Generalized Verma module Isotypic component Kazhdan-Lusztig polynomial Verma module K-module g 6-j symbol 9-j symbol Adjoint representation of a Lie group Antifundamental representation Blattner's conjecture Borel-Weil theorem Borel-Weil-Bott theorem Capelli's identity Casimir invariant Clebsch-Gordan coefficients Coadjoint representation Discrete series representation Harish-Chandra character Harish-Chandra class Harish-Chandra module Infinitesimal character Kirillov character formula Langlands classification Langlands group Maximal torus Orbit method Racah W-coefficient Representation of a Lie group Representation theory of the Galilean group Representation theory of the Lorentz group Representation theory of the Poincaré group Unitarian trick Weyl character formula Wigner 3-j symbols Wigner-Eckart theorem Tensor product of algebras Lie algebra representation Representation of a Lie superalgebra

General information

Categorization	Also known as
Mathematics (under construction)

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