Arithmetic groups

Harish-Chandra functors play a prominent role in the representation theory of reductive groups over finite fields, as they allow one to pass efficiently between representations of a group and those of its Levi subgroups. In this talk I will describe a generalisation of these functors that is more suitable for reductive groups over compact discrete valuation rings and can be applied to study representations of arithmetic groups. This is a joint work with Tyrone Crisp and Ehud Meir.