5 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…

Permutation-module decomposition conjecture. For each $w \in \mathcal G_h^k$, there is $\widehat{\sigma}_{w,h} \in M(\sigma_{w,h})$ such that $M(\widehat{\sigma}_{w,h})$ is a permu…

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…

Let $G$ be a finite group, let $V$ be a permutation $\mathbb{Z}G$-module, meaning that $V$ is a free $\mathbb{Z}$-module with a basis preserved by the action of $G$, and let…