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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 — 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 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
Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… … 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
Invariant subspace — In mathematics, an invariant subspace of a linear mapping : T : V rarr; V from some vector space V to itself is a subspace W of V such that T ( W ) is contained in W . An invariant subspace of T is also said to be T invariant.If W is T invariant … Wikipedia
Cuspidal representation — In number theory, cuspidal representations are certain representations of algebraic groups that occur discretely in L2 spaces. The term cuspidal is derived, at a certain distance, from the cusp forms of classical modular form theory. In the… … Wikipedia
Schröder–Bernstein theorems for operator algebras — The Schröder–Bernstein theorem, from set theory, has analogs in the context operator algebras. This article discusses such operator algebraic results. For von Neumann algebras Suppose M is a von Neumann algebra and E , F are projections in M. Let … Wikipedia
Covering groups of the alternating and symmetric groups — In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective representations of the alternating and symmetric groups. The covering groups were… … Wikipedia
Trivial representation — In the mathematical field of representation theory, a trivial representation is a representation ( V , phi; ) of a group G on which all elements of G act as the identity mapping of V . A trivial representation of an associative or Lie algebra is… … Wikipedia
