5 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…

For an integer $p\,{\geqslant}\, 2$, let $\mathscr{C}^+_p$ be the indicated tensor subcategory of modules for the Lusztig-limit quantum group, and let ${\mathcal{LM}}(1,p)$ denote…

Let $p\,{\geqslant}\, 2$ be an integer. Consider the “long” screening extension of $\overline{\mathscr{U}}_{\mathfrak{q}}s\ell(2)$, namely the Lusztig limit…