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, tempered representation, smooth representation
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 20 Group theory and generalizations
Depositing User:	Professor Roger Plymen
Date Deposited:	10 Dec 2013
Last Modified:	08 Nov 2017 18:18
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/2078

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