3 problems

Let $G$ be the reductive group, let $I$ be an Iwahori subgroup, and let $\rep_{-\kappa}^I$ denote the corresponding category of Iwahori-equivariant modules at level $-\kappa$. Let…

Fix a positive level $\kappa$, set $q=\operatorname{exp}\left(\frac{\pi\sqrt{-1}}{\kappa'-\kappa_{\textup{crit}}}\right)$, and let $M$ be a $U^{\textup{Lus}}_q(\mathfrak{g})$-modul…

Let $\hat{\mathfrak{g}}_{\kappa}\textup{-mod}^{G(\mathcal{O})}$ be the category of $G(\mathcal{O})$-equivariant modules for the affine Kac–Moody algebra at level $\kappa$, and let…