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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.

Contents

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
  • 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 operator
  • 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 theorem, Borel–Weil–Bott theorem

    • Representation theory of algebras

  • Algebra representation
  • Representation theory of Hopf algebras

    • References

    List of representation theory topics Wikipedia
    (Text) CC BY-SA


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