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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 : for Haar measure μ with μ(''G'') = 1. When ''G'' is finite it is given by : 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
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