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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 Kostant partition function ： ウィキペディア英語版 Kostant partition function In representation theory, a branch of mathematics, the Kostant partition function, introduced by , of a root system $\backslash Delta$ is the number of ways one can represent a vector (weight) as an integral non-negative sum of the positive roots $\backslash Delta^+\backslash subset\backslash Delta$. Kostant used it to rewrite the Weyl character formula for the multiplicity of a weight of an irreducible representation of a semisimple Lie algebra. The Kostant partition function can also be defined for Kac–Moody algebras and has similar properties. ==Relation to the Weyl character formula== The values of Kostant's partition function are given by the coefficients of the power series expansion of :$\backslash frac)\}$ where the product is over all positive roots. Using Weyl's denominator formula :$w(e^)\; =\; e^\backslash prod\_(1-e^)\},$ shows that the Weyl character formula :$\backslash operatorname(V)=w(e^)\; \backslash over\; \backslash sum\_\; (-1)^w(e^)\}$ can also be written as :$\backslash operatorname(V)=w(e^)\; \backslash over\; e^\backslash prod\_(1-e^)\}.$ This allows the multiplicities of finite-dimensional irreducible representations in Weyl's character formula to be written as a finite sum involving values of the Kostant partition function, as these are the coefficients of the power series expansion of the denominator of the right hand side. 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「Kostant partition function」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.