翻訳と辞書 Words near each other ・ Harish Naval ・ Harish Patel ・ Harish Raghavendra ・ Harish Raj ・ Harish Raut ・ Harish Rawat ・ Harish Saluja ・ Harish Salve ・ Harish Shankar ・ Harish Sharma ・ Harish Uthaman ・ Harish Verma ・ Harish, Iran ・ Harish, Israel ・ Harish-Chandra ・ Harish-Chandra character ・ Harish-Chandra class ・ Harish-Chandra homomorphism ・ Harish-Chandra isomorphism ・ Harish-Chandra module ・ Harish-Chandra Research Institute ・ Harish-Chandra theorem ・ Harish-Chandra transform ・ Harish-Chandra's c-function ・ Harish-Chandra's function ・ Harish-Chandra's regularity theorem ・ Harish-Chandra's Schwartz space ・ Harish-Chandra's Ξ function ・ Harishankar Brahma ・ Harishankar Parsai Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

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 character ： ウィキペディア英語版 Harish-Chandra character In mathematics, the Harish-Chandra character, named after Harish-Chandra, of a representation of a semisimple Lie group ''G'' on a Hilbert space ''H'' is a distribution on the group ''G'' that is analogous to the character of a finite-dimensional representation of a compact group. ==Definition== Suppose that π is an irreducible unitary representation of ''G'' on a Hilbert space ''H''. If ''f'' is a compactly supported smooth function on the group ''G'', then the operator on ''H'' :$\backslash pi(f)\; =\; \backslash int\_Gf(x)\backslash pi(x)\backslash ,dx$ is of trace class, and the distribution :$\backslash Theta\_\backslash pi:f\backslash mapsto\; \backslash operatorname(\backslash pi(f))$ is called the character (or global character or Harish-Chandra character) of the representation. The character Θπ is a distribution on ''G'' that is invariant under conjugation, and is an eigendistribution of the center of the universal enveloping algebra of ''G'', in other words an invariant eigendistribution, with eigenvalue the infinitesimal character of the representation π. Harish-Chandra's regularity theorem states that any invariant eigendistribution, and in particular any character of an irreducible unitary representation on a Hilbert space, is given by a locally integrable function. 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 character」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.