2 problems

Let $(W,S)$ be a universal Coxeter system of rank $n$, let $\mathcal{J}_{\ne e}$ be its nontrivial two-sided cell, and for each $s\in S$ let $\mathcal{H}_s$ be the diagonal $H$-cel…

Let $(W,S)$ be a universal Coxeter system of rank $n$, and let $\mathcal{J}_{\ne e}$ be its nontrivial two-sided cell. Let $\mathcal{A}_{\mathcal{J}_{\ne e}}$ denote the associated…