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Representation Theory

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Dimensions of some locally analytic representations

Authors: Tobias Schmidt and Matthias Strauch
Journal: Represent. Theory 20 (2016), 14-38
MSC (2010): Primary 11E95, 22E50; Secondary 11S80, 16S30
Published electronically: February 2, 2016
MathSciNet review: 3455080
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Abstract: Let $G$ be the group of points of a split reductive group over a finite extension of $\mathbb {Q}_p$. In this paper, we compute the dimensions of certain classes of locally analytic $G$-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on $p$-adic symmetric spaces. As an application, we compute the dimensions of the unitary $\textrm {GL}_2(\mathbb {Q}_p)$-representations appearing in Colmez’ $p$-adic local Langlands correspondence.

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Additional Information

Tobias Schmidt
Affiliation: Institute de Recherche Mathématique de Rennes, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes, France

Matthias Strauch
Affiliation: Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405
MR Author ID: 620508

Received by editor(s): December 18, 2014
Received by editor(s) in revised form: November 17, 2015, and December 11, 2015
Published electronically: February 2, 2016
Additional Notes: The first author would like to acknowledge support of the Heisenberg programme of Deutsche Forschungsgemeinschaft
The second author would like to acknowledge the support of the National Science Foundation (award DMS-1202303).
Article copyright: © Copyright 2016 American Mathematical Society