正则幂零Hessenberg变分与Schubert多项式的上同调环

Pub Date : 2018-01-24 DOI:10.3792/PJAA.94.87

T. Horiguchi

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引用次数: 3

摘要

本文研究了正则幂零Hessenberg变量的上同环与Schubert多项式之间的关系。为了描述正则幂零Hessenberg变量的上同环的显式表示，Abe-Harada-Horiguchi-Masuda引入了多项式$f_{i,j}$。我们证明了每个多项式$f_{i,j}$是某些舒伯特多项式的交替和。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials

In this paper we study a relation between the cohomology ring of a regular nilpotent Hessenberg variety and Schubert polynomials. To describe an explicit presentation of the cohomology ring of a regular nilpotent Hessenberg variety, polynomials $f_{i,j}$ were introduced by Abe-Harada-Horiguchi-Masuda. We show that every polynomial $f_{i,j}$ is an alternating sum of certain Schubert polynomials.

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