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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 Schubert polynomial ： ウィキペディア英語版 Schubert polynomial In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by and are named after Hermann Schubert. ==Background== described the history of Schubert polynomials. The Schubert polynomials $\backslash mathfrak\_w$ are polynomials in the variables $\backslash \; x\_1,x\_2,\backslash ldots$ depending on an element $w$ of the infinite symmetric group $S\_\backslash infty$ of all permutations of $1,\; 2,\; 3,\backslash ldots$ fixing all but a finite number of elements. They form a basis for the polynomial ring $\backslash mathbb()$ in infinitely many variables. The cohomology of the flag manifold $\backslash text(m)$ is $\backslash mathbb()/I$, where $I$ is the ideal generated by homogeneous symmetric functions of positive degree. The Schubert polynomial $\backslash mathfrak\_w$ is the unique homogeneous polynomial of degree $\backslash ell(w)$ representing the Schubert cycle of $w$ in the cohomology of the flag manifold $\backslash text(m)$ for all sufficiently large $m$. 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「Schubert polynomial」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.