4 problems

Let $n=2r+1$, let $\boldsymbol{c}_{\lambda}^{\jmath}$ be the two-sided cell associated with a special partition $\lambda$ of $2d+1$ with at most $n$ parts, and consider semistandar…

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 $W_f$ be a finite Coxeter group, and let $x,y\in W_f$. Say that $x$ and $y$ have the same generalized $\widetilde{\tau}$-invariant when they are equivalent under all the relati…