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복소기하학연구단
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Permutation Module Decomposition of the Second Cohomology of a Regular Semisimple Hessenberg Variety

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Title
Permutation Module Decomposition of the Second Cohomology of a Regular Semisimple Hessenberg Variety
Author(s)
Cho, Soojin; Jaehyun Hong; Eunjeong Lee
Publication Date
2023-12
Journal
International Mathematics Research Notices, v.2023, no.24, pp.22004 - 22044
Publisher
Oxford University Press
Abstract
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 Bialynicki-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 module to form a permutation module decomposition. Our construction is consistent with a known combinatorial result by Chow on chromatic quasisymmetric functions.
URI
https://pr.ibs.re.kr/handle/8788114/14521
DOI
10.1093/imrn/rnac328
ISSN
1073-7928
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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