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The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials. (English) Zbl 1415.14019

Summary: 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 T. Abe et al. [“Hessenberg varieties and hyperplane arrangements”, Preprint, arXiv:1611.00269]. We show that every polynomial \(f_{i,j}\) is an alternating sum of certain Schubert polynomials.

MSC:

14N15 Classical problems, Schubert calculus
14M15 Grassmannians, Schubert varieties, flag manifolds
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References:

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