This is a list of representation theory topics, by Wikipedia page. See also list of harmonic analysis topics, which is more directed towards the mathematical analysis aspects of representation theory. See also: Glossary of representation theory
General representation theory Linear representation Unitary representation Trivial representation Irreducible representation Semisimple Complex representation Real representation Quaternionic representation Pseudo-real representation Symplectic representation Schur's lemma Restricted representation
Representation theory of groups Group representation Group ring Maschke's theorem Regular representation Character (mathematics) Character theory Class function Representation theory of finite groups Modular representation theory Frobenius reciprocity Restricted representation Induced representation Peter–Weyl theorem Young tableau Spherical harmonic Hecke operator Representation theory of the symmetric group Representation theory of diffeomorphism groups Permutation representation Affine representation Projective representation Central extension
Representation theory of Lie groups and Lie algebras
Representation of a Lie group Lie algebra representation, Representation of a Lie superalgebra Universal enveloping algebra Casimir element Infinitesimal character Harish-Chandra homomorphism Fundamental representation Antifundamental representation Bifundamental representation Adjoint representation Weight (representation theory) Cartan's theorem Spinor Wigner's classification, Representation theory of the Poincaré group Wigner–Eckart theorem Stone–von Neumann theorem Orbit method Kirillov character formula Weyl character formula Discrete series representation Principal series representation Borel–Weil–Bott theorem
Representation theory of algebras Algebra representation Representation theory of Hopf algebras Quiver (mathematics)