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The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials (1801.07930v1)
Published 24 Jan 2018 in math.AG, math.AT, and math.CO
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.