2 problems

Assume $q\neq0$. Let $\operatorname{\mathcal{H}}_n^{\operatorname{aff}}$ be the affine Hecke algebra containing $\operatorname{\mathcal{H}}_n$ and the Laurent polynomial ring in…

For a partition $\lambda$ of $n$, let $\nu_\lambda$ denote the associated symmetrized shuffling operator in $\operatorname{\mathbb{R}}[\mathfrak{S}_n]$. The two relevant families a…