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Algebra Seminar
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Peter Schneider
Universität Munster

Banach space representations of p-adic groups

Friday 28th, March 12:05-12:55pm, Stephen Roberts.

Let F be a p-adic number field. The Langlands philosophy relates l-adic Galois representations over F, for l different from p, to (smooth) complex representations of reductive groups over F. But this picture is not sufficiently rich to understand the p-adic Galois representations. It rather seems necessary to embed it into a much broader picture of a continuous representation theory of G in F-vector spaces. Teitelbaum and I have embarked since a few years on a long term project in this direction. In this lecture I will discuss the notion of a continuous Banach space representation. In particular I will introduce a certain finiteness condition (called admissibility) which allows to completely algebraize the theory. Secondly I will analyze a certain series of explicit representations constructed via parabolic induction.