List of representation theory topics

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

Representation theory of algebras

 * Algebra representation
 * Representation theory of Hopf algebras