6 problems

Gordon–Martino conjecture. There is a natural identification of the $CM_{\bf c}$-partition and the $KL_{\bf L}$-partition, induced by attaching a $KL_{\bf L}$-cell to an irreducibl…

Sommers's cell-region decomposition conjecture.

Canonical cell conjecture. The element of minimal length is unique, and $J(\lambda)$ is a completely prime maximal ideal of ${\mathbf U}({^L \mathfrak{g}})$ whose associated variet…

Let $W$ be a Coxeter group with generating set $S$, and identify weight functions with integer points in a Euclidean space $V$ whose coordinates are their values on the conjugacy c…

Let $\Phi^+$ be the set of positive roots, with short and long roots distinguished, and define … by $\nu(\alpha)=0$ if $\alpha$ is short and $\nu(\alpha)=1$ if $\alpha$ is long. Le…

Let $W$ be a Coxeter group with generating set $S$, and let $C\subset W$ be a cell. Write $\mathtt{Red}(C)$ for the language of reduced expressions of elements of $C$. Casselman's…