List of representation theory topics

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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

## Contents

* 1 General representation theory
* 2 Representation theory of groups
* 3 Representation theory of Lie groups and Lie algebras
* 4 Representation theory of algebras

## 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

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