Categorical actions from Lusztig induction and restriction on finite general linear groups

Abstract

In this note we explain how Lusztig's induction and restriction functors yield categorical actions of Kac–Moody algebras on the derived category of unipotent representations. We focus on the example of finite general linear groups and induction/restriction associated with split Levi subgroups, providing a derived analogue of Harish–Chandra induction/restriction as studied by Chuang–Rouquier in [5].