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Analytic vectors in continuous p-adic representations

Published online by Cambridge University Press:  01 January 2009

Tobias Schmidt*
Affiliation:
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, D-48149 Münster, Germany (email: [email protected])
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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.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2009

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