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Analytic vectors in continuous p-adic representations

Part of: Algebraic number theory: local and $p$-adic fields Discontinuous groups and automorphic forms Lie groups

Published online by Cambridge University Press:  01 January 2009

Tobias Schmidt
Tobias Schmidt*
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany (email: toschmid@math.uni-muenster.de)
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Abstract

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Given a compact p-adic Lie group G over a finite unramified extension L/ℚp let GL/ℚp be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic GL/ℚp-representations that coincides with passage to analytic vectors in the case L=ℚp. On the other hand, we study the functor ‘passage to analytic vectors’ and its derived functors over general basefields. As an application we compute the higher analytic vectors in certain locally analytic induced representations.

Keywords

p-adic Lie groupsrepresentation theoryanalytic vector

MSC classification

Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields 11S99: None of the above, but in this section 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 1 , January 2009 , pp. 247 - 270
Copyright
Copyright © Foundation Compositio Mathematica 2009

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