Locally analytic vectors in representations of locally p-adic analytic groups

Details Locally analytic vectors in representations of locally p-adic analytic groups Locally analytic vectors in representations of locally p-adic analytic groups

2004-05-07

arxiv.org/abs/math/0405137v1

Mathematics

Representation Theory

Draft dated May 4, 2004 135 pages

Scientific paper

This paper develops various foundational results in the locally analytic representation theory of p-adic groups. In particular, we define the functor ``pass to locally analytic vectors'', which attaches to any continuous representation of a p-adic analytic group on a locally convex p-adic topological vector space the associated space of locally analytic vectors. Using this functor, and the point of view that its construction suggests, we establish some basic facts about admissible locally analytic representations (as defined by Schneider and Teitelbaum). We also introduce the related notion of essentially admissible locally analytic representations.

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