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. We define a subset of the Białynicki-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.
This work was supported by the National Research Foundation of Korea [NRF-2020R1A2C1A01011045 to S.C.]; the Institute for Basic Science [IBS-R032-D1 to J.H.]; and the Institute for Basic Science [IBS-R003-D1 to E.L.]. Acknowledgments
