6 problems

Let $W_n^{\mathsf{BC}}$ be the type $\mathrm{B}$ Coxeter group equipped with a weight function determined by a parameter $s$, and let its cells be the Kazhdan–Lusztig cells. The do…

Conjecture B. For any $w,w'\in W_n$, $w\sim_{\mathcal L}w'$ if and only if $Q^{r-1}(w)=M(Q^{r-1}(w'),C)$ for a set $C$ of open cycles; the analogous statement holds for right cells…

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…

Bonnafé–Iancu–Geck–Lam conjecture. For $w \in W_n$ and $r \in \mathbb{Z}_{\geq 0}$,

Let $W_n$ be the Weyl group of type $B_n$, let $r\geq 0$, and let $?\in\{L,R,LR\}$. For $x,y\in W_n$, write $x\sim_{?}^r y$ for the corresponding equivalence relation defined by do…

Let $a,b$ be the parameters defining the relevant Kazhdan–Lusztig cells, let $r\geq 1$, and let signed permutations lie in $B_n$. Two signed permutations are $r$-cycle equivalent (…