English

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

Representation Theory 2007-05-23 v1 Number Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0405137,
  title  = {Locally analytic vectors in representations of locally p-adic analytic groups},
  author = {Matthew Emerton},
  journal= {arXiv preprint arXiv:math/0405137},
  year   = {2007}
}

Comments

Draft dated May 4, 2004 135 pages

R2 v1 2026-07-22T17:05:13.232Z