Locally analytic distributions and p-adic representation theory, with applications to GL₂

1999/12/09 by Peter Schneider, Schneider, Peter, Jeremy Teitelbaum +1 · 4 citations
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.math/9912073

35 pages

arxiv created 1999/12/09 · openalex publication_date 1999/12/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex K-vector spaces. We call the objects of this category "admissible" representations and we establish some of their basic properties. Most importantly we show that (at least when G is compact) the category of admissible representations in our sense can be algebraized; it is faithfully full (anti)-embedded into the category of modules over the locally analytic distribution algebra D(G,K) of G over K. As an application of our theory, we prove the topological irreducibility of generic members of the p-adic principal series of GL(2,Qp).

Cited by

• Towards a finite-slope universal Rankin-Selberg p-adic L-function
• On some non-principal locally analytic representations induced by Whittaker modules
• Locally analytic completed cohomology of Shimura varieties of Hodge type
• A fully faithful p-adic Riemann-Hilbert functor for coadmissible D-cap-modules

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