An additive basis for the cohomology rings of regular nilpotent Hessenberg varieties

Abstract

In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincaré duals of smaller regular nilpotent Hessenberg varieties. In particular, all of the Poincaré duals of smaller regular nilpotent Hessenberg varieties in the given regular nilpotent Hessenberg variety are linearly independent.