Dimensions of some locally analytic representations
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- by Tobias Schmidt and Matthias Strauch
- Represent. Theory 20 (2016), 14-38
- DOI: https://doi.org/10.1090/ert/475
- Published electronically: February 2, 2016
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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.References
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Bibliographic 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