2 problems

For $n\geq 0$, let $S_n$ be the symmetric group, let $\mathrm{Inv}_n$ be its set of involutions, and let $\mathbf{K}_n(w)=-$ mean that Kostant's problem for the simple highest weig…

Let $W$ be the Weyl group, let $\boldsymbol{R}$ be a right cell, and let $\widehat{\boldsymbol{R}}=\{x\in W:x\leq_{\mathtt{R}}w\text{ for some }w\in\boldsymbol{R}\}$. Let…