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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 Discrete series representation ： ウィキペディア英語版 Discrete series representation In mathematics, a discrete series representation is an irreducible unitary representation of a locally compact topological group ''G'' that is a subrepresentation of the left regular representation of ''G'' on L²(''G''). In the Plancherel measure, such representations have positive measure. The name comes from the fact that they are exactly the representations that occur discretely in the decomposition of the regular representation. ==Properties== If ''G'' is unimodular, an irreducible unitary representation ρ of ''G'' is in the discrete series if and only if one (and hence all) matrix coefficient :$\backslash langle\; \backslash rho(g)\backslash cdot\; v,\; w\; \backslash rangle\; \backslash ,$ with ''v'', ''w'' non-zero vectors is square-integrable on ''G'', with respect to Haar measure. When ''G'' is unimodular, the discrete series representation has a formal dimension ''d'', with the property that :$d\backslash int\; \backslash langle\; \backslash rho(g)\backslash cdot\; v,\; w\; \backslash rangle\; \backslash overlinedg\; =\backslash langle\; v,\; x\; \backslash rangle\backslash overline$ for ''v'', ''w'', ''x'', ''y'' in the representation. When ''G'' is compact this coincides with the dimension when the Haar measure on ''G'' is normalized so that ''G'' has measure 1. 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「Discrete series representation」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.