
Peter Schneider
Universität Munster
Banach space representations of padic groups
Friday 28th, March 12:0512:55pm,
Stephen Roberts.
Let F be a padic number field. The Langlands
philosophy relates ladic 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 padic Galois representations.
It rather seems necessary to embed it into a much broader
picture of a continuous representation theory of G in Fvector 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.







