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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.
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