The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2018-01-24 DOI:10.3792/PJAA.94.87

T. Horiguchi

引用次数: 3

Abstract

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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正则幂零Hessenberg变分与Schubert多项式的上同调环

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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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.