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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Harish-Chandra module ： ウィキペディア英語版 Harish-Chandra module In mathematics, specifically in the representation theory of Lie groups, a Harish-Chandra module, named after the Indian mathematician and physicist Harish-Chandra, is a representation of a real Lie group, associated to a general representation, with regularity and finiteness conditions. When the associated representation is a $(\backslash mathfrak,K)$-module, then its Harish-Chandra module is a representation with desirable factorization properties. ==Definition== Let ''G'' be a Lie group and ''K'' a compact subgroup of ''G''. If $(\backslash pi,V)$ is a representation of ''G'', then the ''Harish-Chandra module'' of $\backslash pi$ is the subspace ''X'' of ''V'' consisting of the K-finite smooth vectors in ''V''. This means that ''X'' includes exactly those vectors ''v'' such that the map $\backslash varphi\_v\; :\; G\; \backslash longrightarrow\; V$ via :$\backslash varphi\_v(g)\; =\; \backslash pi(g)v$ is smooth, and the subspace :$\backslash text\backslash$ is finite-dimensional. 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「Harish-Chandra module」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.