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A canonical dimension estimate for non-split semisimple $p$-adic Lie groups

Authors: Konstantin Ardakov and Christian Johansson
Journal: Represent. Theory 20 (2016), 128-138
MSC (2010): Primary 11F85, 16S99, 22E50
Published electronically: February 18, 2016
MathSciNet review: 3461051
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Abstract: We prove that the canonical dimension of an admissible Banach space or a locally analytic representation of an arbitrary semisimple $p$-adic Lie group is either zero or at least half the dimension of a non-zero coadjoint orbit. This extends the results of Ardakov, Wadsley, and Schmidt in the split semisimple case.

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Additional Information

Konstantin Ardakov
Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom

Christian Johansson
Affiliation: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
MR Author ID: 1031168

Keywords: $p$-adic Banach space representations, locally analytic representations, canonical dimension
Received by editor(s): July 6, 2015
Received by editor(s) in revised form: December 31, 2015
Published electronically: February 18, 2016
Article copyright: © Copyright 2016 American Mathematical Society