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