The cohomology rings of regular semisimple Hessenberg varieties for $h=(h(1),n,\ldots,n)$

Hiraku Abe; Tatsuya Horiguchi; Mikiya Masuda

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arXiv · 1704.00934

The cohomology rings of regular semisimple Hessenberg varieties for $h=(h(1),n,\ldots,n)$

Hiraku Abe·Tatsuya Horiguchi·Mikiya Masuda

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Abstract

We investigate the cohomology rings of regular semisimple Hessenberg varieties whose Hessenberg functions are of the form $h=(h(1),n\dots,n)$ in Lie type $A_{n-1}$. The main result of this paper gives an explicit presentation of the cohomology rings in terms of generators and their relations. Our presentation naturally specializes to Borel's presentation of the cohomology ring of the flag variety and it is compatible with the representation of the symmetric group $\mathfrak{S}_n$ on the cohomology constructed by J. Tymoczko. As a corollary, we also give an explicit presentation of the $\mathfrak{S}_n$-invariant subring of the cohomology ring.

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BibTeX RIS

Hiraku Abe, Tatsuya Horiguchi, Mikiya Masuda. 2017-04-04. The cohomology rings of regular semisimple Hessenberg varieties for $h=(h(1),n,\ldots,n)$. https://arxiv.org/abs/1704.00934

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