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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 Frobenius–Schur indicator ： ウィキペディア英語版 Frobenius–Schur indicator In mathematics the Schur indicator, named after Issai Schur, or Frobenius–Schur indicator describes what invariant bilinear forms a given irreducible representation of a compact group on a complex vector space has. It can be used to classify the irreducible representations of compact groups on real vector spaces. ==Definition== If a finite-dimensional continuous complex representation of a compact group ''G'' has character χ its Frobenius–Schur indicator is defined to be :$\backslash int\_\backslash chi(g^2)\backslash ,d\backslash mu$ for Haar measure μ with μ(''G'') = 1. When ''G'' is finite it is given by :$\backslash sum\_\backslash chi(g^2).$ The Frobenius–Schur indicator is always 1, 0, or -1. It provides a criterion for deciding whether an irreducible representation of ''G'' is real, complex or quaternionic, in a specific sense defined below. Below we discuss the case of finite groups, but the general compact case is completely analogous. 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「Frobenius–Schur indicator」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.