Unicity of types for supercuspidal representations of p-adic SL2

Tools

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

Preview

PDF (Latham (2016)) - Published Version
Download (416kB) | Preview

Abstract

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
Related URLs:	http://www.scopus.com/inward/record.url?...
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

Downloads

Downloads per month over past year

Actions (login required)

View Item