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The cohomology rings of regular nilpotent Hessenberg varieties
Megumi Harada, Tatsuya Horiguchi
This manuscript is a contributed chapter in the forthcoming CRC Press volume, titled the Handbook of Combinatorial Algebraic Geometry: Subvarieties of the Flag Variety. The book, a…
Coordinate rings of regular nilpotent Hessenberg varieties in the open opposite Schubert cell
Tatsuya Horiguchi, Tomoaki Shirato
Dale Peterson has discovered a surprising result that the quantum cohomology ring of the flag variety $\mbox{GL}_n(\mathbb{C})/B$ is isomorphic to the coordinate ring of the inters…
Toric orbifolds associated with partitioned weight polytopes in classical types
Tatsuya Horiguchi, Mikiya Masuda, John Shareshian +1
Given a root system of type , , , or in Euclidean space , let be the associated Weyl group. For a point not orthogonal to any of the roots…
A survey of recent developments on Hessenberg varieties
Hiraku Abe, Tatsuya Horiguchi
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In particular, we will see how hyp…
The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope
Megumi Harada, Tatsuya Horiguchi, Mikiya Masuda +1
Regular semisimple Hessenberg varieties are subvarieties of the flag variety arising naturally in the intersection of geometry, representation theory,…
The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials
Tatsuya Horiguchi
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 cohomo…