TYPES AND HECKE ALGEBRAS FOR PRINCIPAL SERIES REPRESENTATIONS OF SPLIT REDUCTIVE P-ADIC GROUPS

We construct types in the sense of Bushnell and Kutzko for principal s eries representations of split connected reductive p-adic groups (with mild restrictions on the residual characteristic) and describe the re sulting Hecke algebras. We discuss their interpretation as Iwahori Hec ke algebras of related reductive groups (in general disconnected). In addition, we describe how (parabolic) induction and (Jacquet) restrict ion functors and questions about square-integrability can be transferr ed to this context. (C) Elsevier, Paris.