Higher Specht bases and $q$-series for the cohomology rings of certain
Hessenberg varieties
Higher Specht bases and $q$-series for the cohomology rings of certain
Hessenberg varieties
It is conjectured (following the Stanley-Stembridge conjecture) that the cohomology rings of regular semisimple Hessenberg varieties yield permutation representations, but the decompositions of the modules are only known in some cases. For the Hessenberg function $h=(h(1),n,\ldots,n)$, the structure of the cohomology ring was determined by Abe, Horiguchi, and Masuda in …