# Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety

@inproceedings{Cho2021PermutationMD, title={Permutation module decomposition of the second cohomology of a regular semisimple Hessenberg variety}, author={Soojin Cho and Jaehyun Hong and Eunjeong Lee}, year={2021} }

. Regular semisimple Hessenberg varieties admit actions of associated Weyl groups on their cohomology spaces of each degree. In this paper, we consider the module structure of the cohomology spaces of regular semisimple Hessenberg varieties of type A . We deﬁne a subset of the Bia lynicki-Birula basis of the cohomology space which becomes a module generator set of the cohomology module of each degree. We use these generators to construct permutation submodules of the degree two cohomology…

## 3 Citations

### Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties

- Mathematics
- 2021

It is well-known that the T -fixed points of a Schubert variety in the flag variety GLn(C)/B can be characterized purely combinatorially in terms of Bruhat order on the symmetric group Sn. In a…

### Birational geometry of generalized Hessenberg varieties and the generalized Shareshian-Wachs conjecture

- Mathematics
- 2022

. We introduce generalized Hessenberg varieties and estab-lish basic facts. We show that the Tymoczko action of the symmetric group S n on the cohomology of Hessenberg varieties extends to…

### CLOSURES OF HESSENBERG SCHUBERT CELLS IN REGULAR SEMISIMPLE HESSENBERG VARIETIES

- Mathematics
- 2021

It is well known that the Schubert cells in the flag variety GLn(C)/B satisfies closure relations which can be characterized purely combinatorially in terms of Bruhat order on the symmetric group Sn.…

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