7 problems

Riche–Williamson's p-canonical basis conjecture. The values at $v=1$ of the coefficients ${}^p m_{y,x}$ express the characters of tilting modules in terms of Weyl characters. This…

The p-cell eigenmap conjecture. For every $p$-cell $\lambda$, there exists a chain map

Categorical p-half-twist conjecture. For any $w$ in the $p$-cell $\lambda$,

The p-distinguished involution conjecture. In each left $p$-cell there is a unique involution $d$ such that

The p-canonical half-twist conjecture. For any $w$ in $\lambda$,

Let $W$ be the Weyl group under consideration, and let ${}^{p} \!\mkern 1mu {\mathbf a}_{\mathbf c}:W\to\mathbb{R}_{\ge 0}$ be the function obtained by extending the cell invariant…

Let $\mathbf{G}$ be a reductive algebraic group whose derived subgroup is simply connected, let $\mathbf{B}\subset\mathbf{G}$ be a Borel subgroup, and let…