The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials

The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials

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.sub.i,j] were introduced by Abe-Harada-Horiguchi-Mas...

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Veröffentlicht in:Proceedings of the Japan Academy. Series A. Mathematical sciences 2018-11, Vol.94 (9), p.87-92
1. Verfasser: Horiguchi, Tatsuya
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical research
Polynomials
Rings (Mathematics)
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Zusammenfassung: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.sub.i,j] were introduced by Abe-Harada-Horiguchi-Masuda. We show that every polynomial [f.sub.i,j] is an alternating sum of certain Schubert polynomials.Key words: Flag varieties; Hessenberg varieties; Schubert polynomials.
ISSN:0386-2194
DOI:10.3792/pjaa.94.87