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completely irreducible representation

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  • Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

  • Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… …   Wikipedia

  • Representation theory of SL2(R) — In mathematics, the main results concerning irreducible unitary representations of the Lie group SL2(R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish Chandra (1952). Structure of the complexified Lie algebra We choose a… …   Wikipedia

  • Modular representation theory — is a branch of mathematics, and that part of representation theory that studies linear representations of finite group G over a field K of positive characteristic. As well as having applications to group theory, modular representations arise… …   Wikipedia

  • Regular representation — In mathematics, and in particular the theory of group representations, the regular representation of a group G is the linear representation afforded by the group action of G on itself. ignificance of the regular representation of a groupTo say… …   Wikipedia

  • Projective representation — In the mathematical field of representation theory, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to :PGL( V ,F) = GL( V ,F)/F lowast; where GL( V ,F) is the automorphism group of… …   Wikipedia

  • Unitary representation — In mathematics, a unitary representation of a group G is a linear representation π of G on a complex Hilbert space V such that π( g ) is a unitary operator for every g ∈ G . The general theory is well developed in case G is a locally compact… …   Wikipedia

  • Lie algebra representation — Lie groups …   Wikipedia

  • Frobenius-Schur indicator — In mathematics the Schur indicator, named after Issai Schur, or Frobenius Schur indicator describes what invariant bilinear forms a given irreducible representation of a compact group on a complex vector space has, and can be used to classify the …   Wikipedia

  • Young tableau — In mathematics, a Young tableau (pl.: tableaux ) is a combinatorial object useful in representation theory. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their… …   Wikipedia

  • Gelfand-Naimark-Segal construction — In functional analysis, given a C* algebra A , the Gelfand Naimark Segal construction establishes a correspondence between cyclic * representations of A and certain linear functionals on A (called states ). The correspondence is shown by an… …   Wikipedia

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