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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 Hessenberg variety ： ウィキペディア英語版 Hessenberg variety In geometry, Hessenberg varieties, first studied by De Mari, Procesi, and Shayman, are a family of subvarieties of the full flag variety which are defined by a Hessenberg function ''h'' and a linear transformation ''X''. The study of Hessenberg varieties was first motivated by questions in numerical analysis in relation to algorithms for computing eigenvalues and eigenspaces of the linear operator ''X''. Later work by Springer, Peterson, Kostant, among others, found connections with combinatorics, representation theory and cohomology. == Definitions == A ''Hessenberg function'' is a function of tuples :$h\; :\backslash \; \backslash rightarrow\; \backslash$ where :$h(i+1)\; \backslash geq\; \backslash text(i,h(i))\; \backslash text\; 1\; \backslash leq\; i\; \backslash leq\; n-1.$ For example, :$h(1,2,3,4,5)=(2,3,3,4,5)\; \backslash ,$ is a Hessenberg function. For any Hessenberg function ''h'' and a linear transformation :$X:\; \backslash C^n\; \backslash rightarrow\; \backslash C^n,\; \backslash ,$ the ''Hessenberg variety'' is the set of all flags $F\_$ such that :$X\; \backslash cdot\; F\_i\; \backslash subseteq\; F\_$ for all i. Here $F\_$ denotes the vector space spanned by the first $h(i)$ vectors in the flag $F\_$. :$\backslash mathcal(X,h)\; =\; \backslash \; \backslash subset\; F\_\; \backslash text\; 1\; \backslash leq\; i\; \backslash leq\; n\; \backslash \}$ 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「Hessenberg variety」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.