admissible representation

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English-Russian scientific dictionary. 2008.

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  • Admissible representation — In mathematics, admissible representations are a well behaved class of representations used in the representation theory of reductive Lie groups over real or p adic fields. They were introduced by Harish Chandra.Real reductive groupsFor real… …   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 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

  • Tempered representation — In mathematics, a tempered representation of a linear semisimple Lie group is a representation that has a basis whose matrix coefficients lie in the L p space : L 2+ epsilon;( G ) for any epsilon; gt; 0. FormulationThis condition, as just given,… …   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

  • Gelfand pair — In mathematics, the expression Gelfand pair refers to a pair ( G ,  K ) consisting of a group G and a subgroup K that satisfies a certain property on restricted representations.When G is a finite group the simplest definition is, roughly speaking …   Wikipedia

  • Langlands classification — In mathematics, the Langlands classification is a classification of irreducible representations of a reductive Lie group G , suggested by Robert Langlands (1973). More precisely, it classifies the irreducible admissible ( g , K ) modules,for g a… …   Wikipedia

  • List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …   Wikipedia

  • Multiplicity-one theorem — In the mathematical theory of automorphic representations, a multiplicity one theorem is a result about the representation theory of an adelic reductive algebraic group. The multiplicity in question is the number of times a given abstract group… …   Wikipedia

  • Harish-Chandra — for|the character in Hindu mythology|HarishchandraHarish Chandra (11 October 1923 16 October 1983) was an Indian born American mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups …   Wikipedia

  • GÉOMÉTRIE DIFFÉRENTIELLE CLASSIQUE — L’histoire des courbes planes est intimement liée à l’histoire et aux développements du calcul infinitésimal, et les premiers résultats obtenus au XVIIe siècle sont directement issus de considérations géométriques et cinématiques (cf. CALCUL… …   Encyclopédie Universelle

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