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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Dimensions of some locally analytic representations
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by Tobias Schmidt and Matthias Strauch PDF
Represent. Theory 20 (2016), 14-38 Request permission

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
  • Email: Tobias.Schmidt@univ-rennes1.fr
  • Matthias Strauch
  • Affiliation: Department of Mathematics, Indiana University, Rawles Hall, Bloomington, Indiana 47405
  • MR Author ID: 620508
  • Email: mstrauch@indiana.edu
  • 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).
  • © Copyright 2016 American Mathematical Society
  • Journal: Represent. Theory 20 (2016), 14-38
  • MSC (2010): Primary 11E95, 22E50; Secondary 11S80, 16S30
  • DOI: https://doi.org/10.1090/ert/475
  • MathSciNet review: 3455080