algebraically 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

• Representation ring — In mathematics, especially in the area of algebra known as representation theory, the representation ring of a group is a ring formed from all the (isomorphism classes of the) linear representations of the group. For a given group, the ring will… …   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

• 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

• Absolutely irreducible — In mathematics, absolutely irreducible is a term applied to linear representations or algebraic varieties over a field. It means that the object in question remains irreducible, even after any finite extension of the field of coefficients. In… …   Wikipedia

• Spectrum of a C*-algebra — The spectrum of a C* algebra or dual of a C* algebra A, denoted Â, is the set of unitary equivalence classes of irreducible * representations of A. A * representation π of A on a Hilbert space H is irreducible if, and only if, there is no closed… …   Wikipedia

• Deligne–Lusztig theory — In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ adic cohomology with compact support, introduced by Deligne Lusztig (1976). Lusztig (1984) used these representations to… …   Wikipedia

• Character theory — This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media). In mathematics, more specifically in group theory, the character of a group representation is a function… …   Wikipedia