Smooth Representations of p-adic Groups: The Role of Compact Open Subgroups

Abstract

This article concerns the method of investigating the smooth (complex) representations of a reductive p-adic group via the method of restriction to compact open subgroups, and amounts largely to a report on joint work of the author and Kutzko. Let G denote the group of F-points of some connected reductive algebraic group defined over the non-Archimedean local field F. The basic idea of the method is to isolate a family\( F\) of irreducible smooth representations of compact open subgroups of G, and then to describe a given irreducible smooth representation of G in terms of those members of\( F\) that it contains.