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In mathematics, the Langlands classification is a description of the irreducible representations of a reductive Lie group ''G'', suggested by Robert Langlands (1973). There are two slightly different versions of the Langlands classification. One of these describes the irreducible admissible (''g'',''K'')-modules, for ''g'' a Lie algebra of a reductive Lie group ''G'', with maximal compact subgroup ''K'', in terms of tempered representations of smaller groups. The tempered representations were in turn classified by Anthony Knapp and Gregg Zuckerman. The other version of the Langlands classification divides the irreducible representations into L-packets, and classifies the L-packets in terms of certain homomorphisms of the Weil group of R or C into the Langlands dual group. ==Notation== *''g'' is the Lie algebra of a real reductive Lie group ''G'' in the Harish-Chandra class. *''K'' is a maximal compact subgroup of ''G'', with Lie algebra ''k''. *ω is a Cartan involution of ''G'', fixing ''K''. *''p'' is the −1 eigenspace of a Cartan involution of ''g''. *''a'' is a maximal abelian subspace of ''p''. *Σ is the root system of ''a'' in ''g''. *Δ is a set of simple roots of Σ. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Langlands classification」の詳細全文を読む スポンサード リンク
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