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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 Eisenstein integral ： ウィキペディア英語版 Eisenstein integral In mathematical representation theory, the Eisenstein integral is an integral introduced by in the representation theory of semisimple Lie groups, analogous to Eisenstein series in the theory of automorphic forms. used Eisenstein integrals to decompose the regular representation of a semisimple Lie group into representations induced from parabolic subgroups. gave a survey of Harish-Chandra's work on this. ==Definition== defined the Eisenstein integral by :$\backslash displaystyle\; E(P:\backslash psi:\backslash nu:x)\; =\; \backslash int\_K\backslash psi(xk)\backslash tau(k^)\backslash exp((i\backslash nu-\backslash rho\_P)H\_P(xk))\; \backslash ,\; dk$ where: *''x'' is an element of a semisimple group ''G'' *''P'' = ''MAN'' is a cuspidal parabolic subgroup of ''G'' *ν is an element of the complexification of ''a'' *''a'' is the Lie algebra of ''A'' in the Langlands decomposition ''P'' = ''MAN''. *''K'' is a maximal compact subgroup of ''G'', with ''G'' = ''KP''. *ψ is a cuspidal function on ''M'', satisfying some extra conditions *τ is a finite-dimensional unitary double representation of ''K'' *''H''''P''(''x'') = log ''a'' where ''x'' = ''kman'' is the decomposition of ''x'' in ''G'' = ''KMAN''. 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「Eisenstein integral」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.