## 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

### Keywords:

flag varieties; Hessenberg varieties; Schubert polynomials
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### References:

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