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The unicity of types for depth-zero supercuspidal representations


Author: Peter Latham
Journal: Represent. Theory 21 (2017), 590-610
MSC (2010): Primary 22E50
DOI: https://doi.org/10.1090/ert/511
Published electronically: December 13, 2017
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Abstract: We establish the unicity of types for depth-zero supercuspidal representations of an arbitrary $ p$-adic group $ G$, showing that each depth-zero supercuspidal representation of $ G$ contains a unique conjugacy class of typical representations of maximal compact subgroups of $ G$. As a corollary, we obtain an inertial Langlands correspondence for these representations via the Langlands correspondence of DeBacker and Reeder.


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Additional Information

Peter Latham
Affiliation: Department of Mathematics, University of East Anglia, Norwich, United Kingdom
Email: peter.latham@kcl.ac.uk

DOI: https://doi.org/10.1090/ert/511
Keywords: Theory of types, $p$-adic groups, depth-zero supercuspidals, Langlands correspondence
Received by editor(s): September 13, 2016
Received by editor(s) in revised form: October 3, 2017, and November 9, 2017
Published electronically: December 13, 2017
Article copyright: © Copyright 2017 American Mathematical Society

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