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Representation Theory

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Duality for admissible locally analytic representations

Authors: Peter Schneider and Jeremy Teitelbaum
Journal: Represent. Theory 9 (2005), 297-326
MSC (2000): Primary 11S80, 22E50
Published electronically: April 12, 2005
MathSciNet review: 2133762
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Abstract: We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of $p$-adic analytic group $G$. A naive contragredient does not exist. As a best approximation, we construct an involutive “duality” functor from the bounded derived category of modules over the distribution algebra of $G$ with coadmissible cohomology to itself. on the subcategory corresponding to complexes of smooth representations, this functor induces the usual smooth contragredient (with a degree shift). Although we construct our functor in general we obtain its involutivity, for technical reasons, only in the case of locally $\mathbb {Q}_p$-analytic groups.

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Additional Information

Peter Schneider
Affiliation: Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
MR Author ID: 156590

Jeremy Teitelbaum
Affiliation: Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, 851 S. Morgan St., Chicago, Illinois 60607

Received by editor(s): July 27, 2004
Received by editor(s) in revised form: February 27, 2005
Published electronically: April 12, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.