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On the local Langlands correspondence for non-tempered representations

On the local Langlands correspondence for non-tempered representations
On the local Langlands correspondence for non-tempered representations
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 squareintegrable representations of Levi subgroups of G. We establish the basic properties of these new R-groups, which generalize Knapp–Stein R-groups.
1867-5778
27-50
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4
Aubert, Anne-Marie
f1ab184a-28bd-49a7-bec5-d0abcec2fed0
Baum, Paul
fb630982-847c-4fef-8bd3-b344875be774
Plymen, Roger
76de3dd0-ddcb-4a34-98e1-257dddb731f5
Solleveld, Maarten
87e40b53-0137-45fd-8582-38da531528a4

Aubert, Anne-Marie, Baum, Paul, Plymen, Roger and Solleveld, Maarten (2014) On the local Langlands correspondence for non-tempered representations. Munster Journal of Mathematics, 7, 27-50.

Record type: Article

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 squareintegrable representations of Levi subgroups of G. We establish the basic properties of these new R-groups, which generalize Knapp–Stein R-groups.

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Published date: 22 August 2014
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 369697
URI: https://eprints.soton.ac.uk/id/eprint/369697
ISSN: 1867-5778
PURE UUID: 7df4b116-df9b-42b6-8f65-c4f4494dabe1

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Date deposited: 13 Oct 2014 09:07
Last modified: 17 Jul 2017 21:55

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