On the local Langlands correspondence for non-tempered representations

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2013) On the local Langlands correspondence for non-tempered representations. [MIMS Preprint]

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Abstract

Let $G$ be a reductive $p$-adic group. We study how a local Langlands correspondence for irreducible tempered $G$-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of $G$. We prove that, under a natural condition involving compatibility with unramified twists, this is possible in a canonical way. To this end we introduce analytic R-groups associated to non-tempered essentially square-integrable representations of Levi subgroups of $G$. We establish the basic properties of these new R-groups, which generalize Knapp-Stein R-groups.

Item Type: MIMS Preprint
Uncontrolled Keywords: reductive $p$-adic group, representation theory, R-group, local Langlands conjecture
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory
MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 23 Jul 2013
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1999

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