Unicity of types for supercuspidal representations of p-adic SL2

Latham, Peter (2016) Unicity of types for supercuspidal representations of p-adic SL2. Journal of Number Theory, 162. pp. 376-390. ISSN 0022-314X

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We consider the question of unicity of types on maximal compact subgroups for supercuspidal representations of SL2 over a nonarchimedean local field of odd residual characteristic. We introduce the notion of an archetype as the SL2-conjugacy class of a typical representation of a maximal compact subgroup, and go on to show that any archetype in SL2 is restricted from one in GL2. From this it follows that any archetype must be induced from a Bushnell-Kutzko type. Given a supercuspidal representation π of SL2(F), we give an additional explicit description of the number of archetypes admitted by π in terms of its ramification. We also describe a relationship between archetypes for GL2 and SL2 in terms of L-packets, and deduce an inertial Langlands correspondence for SL2.

Item Type: Article
Additional Information: © 2015 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Uncontrolled Keywords: bushnell-kutzko types,langlands correspondence,p-adic groups,special linear group
Faculty \ School: Faculty of Science > School of Mathematics
Faculty of Science
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Depositing User: Pure Connector
Date Deposited: 12 Jan 2016 12:00
Last Modified: 22 Oct 2022 00:39
URI: https://ueaeprints.uea.ac.uk/id/eprint/56224
DOI: 10.1016/j.jnt.2015.10.008

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