Bases of the equivariant cohomologies of regular semisimple Hessenberg varieties

We consider bases for the cohomology space of regular semisimple Hessenberg varieties, consisting classes that naturally arise from Białynicki-Birula decomposition varieties. give an explicit combinatorial description support each class, which enables us to compute symmetric group actions on in our bases. then successfully apply results permutohedral varieties explicitly write down class and construct permutation submodules constitute summands a degree. This resolves problem posed by Stembridge geometric construction module also conjecture Chow equivariant spaces