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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 Steinberg's formula ： ウィキペディア英語版 Steinberg formula In mathematical representation theory, Steinberg's formula, introduced by , describes the multiplicity of an irreducible representation of a semisimple complex Lie algebra in a tensor product of two irreducible representations. It is a consequence of the Weyl character formula, and for the Lie algebra sl2 it is essentially the Clebsch–Gordan formula. Steinberg's formula states that the multiplicity of the irreducible representation of highest weight ''ν'' in the tensor product of the irreducible representations with highest weights ''λ'' and ''μ'' is given by :$\backslash sum\_\; \backslash epsilon(ww^\backslash prime)P(w(\backslash lambda+\backslash rho)+w^\backslash prime(\backslash mu+\backslash rho)-(\backslash nu+2\backslash rho))$ where ''W'' is the Weyl group, ε is the determinant of an element of the Weyl group, ρ is the Weyl vector, and ''P'' is the Kostant partition function giving the number of ways of writing a vector as a sum of positive roots. ==References== * * 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「Steinberg formula」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.