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 Weyl's character formula