Types and Hecke algebras for principal series representations of split reductive p-adic groups

Abstract

We construct types in the sense of Bushnell and Kutzko for principal series representations of split connected reductive p-adic groups (with mild restrictions on the residual characteristic) and describe the resulting Hecke algebras. We discuss their interpretation as Iwahori Hecke algebras of related reductive groups (in general disconnected). In addition, we describe how (parabolic) induction and (Jacquet) restriction functors and questions about square-integrability can be transferred to this context.