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

2004/05/07 by Matthew Emerton, Emerton, Matthew · 1 citation
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.math/0405137

Draft dated May 4, 2004 135 pages

arxiv created 2004/05/07 · openalex publication_date 2004/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• On the finite length of some p-adic representations of the quaternion algebra over \Q_p

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