## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials

Tatsuya Horiguchi

#### 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.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 9 (2018), 87-92.

Dates
First available in Project Euclid: 1 November 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1541059248

Digital Object Identifier
doi:10.3792/pjaa.94.87

Mathematical Reviews number (MathSciNet)
MR3871391

Subjects
Primary: 14N15: Classical problems, Schubert calculus

#### Citation

Horiguchi, Tatsuya. The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 9, 87--92. doi:10.3792/pjaa.94.87. https://projecteuclid.org/euclid.pja/1541059248

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