3 problems

Assume that ${\mathfrak{g}}$ is of finite type. Let $W$ be the Weyl group, let $i\in I$, let $a\in\mathbb{C}^*$, and let $\boldsymbol{\psi}_{w(\omega_i^\vee),a}$ be the correspondi…

Let $m,n$ be nonnegative integers with $|m-n|$ even. Let $p$ be a nonnegative integer and $r$ an integer with $0\leq r\leq p$. Consider the representation of…

Affine Langlands character conjecture. The polynomial