Runner Removal Morita Equivalences

Abstract

Let $${U}_{q} = {U}_{q}({\mathfrak{g}\mathfrak{l}}_{n})$$ be Lusztig’s divided power quantum general linear group over the complex field with parameter q, a root of unity. We investigate the category of finite-dimensional modules over U q . Lusztig’s famous character formula for simple modules over U q is written purely in terms of the affine Weyl group and its Hecke algebra, which are independent ofq. Our result may be viewed as the categorical version of this independence. Moreover, our methods are valid over fields of positive characteristic. The proof uses the modular representation theory of symmetric groups and finite general linear groups, and the notions of sl2-categorification and perverse equivalences.