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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 Multiplicity-one theorem ： ウィキペディア英語版 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 representation is realised in a certain space, of square integrable functions, given in a concrete way. ==Definition== Let ''G'' be a reductive algebraic group over a number field ''K'' and let A denote the adeles of ''K''. Let ''Z'' denote the centre of ''G'' and let ω be a continuous unitary character from ''Z''(''K'')\Z(A)× to C×. Let ''L''20(''G''(''K'')/''G''(A), ω) denote the space of cusp forms with central character ω on ''G''(A). This space decomposes into a direct sum of Hilbert spaces :$L^2\_0(G(K)\backslash backslash\; G(\backslash mathbf),\backslash omega)=\backslash hat\_m\_\backslash pi\; V\_\backslash pi$ where the sum is over irreducible subrepresentations and ''m''π are non-negative integers. The group of adelic points of ''G'', ''G''(A), is said to satisfy the multiplicity-one property if any smooth irreducible admissible representation of ''G''(A) occurs with multiplicity at most one in the space of cusp forms of central character ω, i.e. ''m''π is 0 or 1 for all such π. 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「Multiplicity-one theorem」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.