3 problems

Let $h\colon [k]\rightarrow [k]$ be a Hessenberg function, let $S$ be a regular semisimple operator on $\mathbb C^k$, and let $\mathfrak S_k$ act on $H^*(\operatorname{Hess}(S,h))$…

Let $k$ be a positive integer, let $h\colon [k]\rightarrow [k]$ be a Hessenberg function, let $S$ be a regular semisimple operator on $\mathbb C^k$, and let $\mathfrak S_k$ act on…

Let $n$ be a positive integer, let $\lambda$ be a partition of $n$, and let $M^\lambda$ be the corresponding permutation module of the symmetric group $\mathcal{S}_n$. The Benson–S…