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Geometric structure for the principal series of a reductive p-adic group with connected centre

Geometric structure for the principal series of a reductive p-adic group with connected centre
Geometric structure for the principal series of a reductive p-adic group with connected centre
Let G be a split reductive p-adic group with connected centre.
We show that each Bernstein block in the principal series of G admits a definite geometric structure, namely that of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form T//W where T is a maximal torus in the Langlands dual group of G and W is the Weyl group of G.
reductive p-adic group, representation theory, geometric structure, local langlands conjecture
1661-6952
663-680
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 (2016) Geometric structure for the principal series of a reductive p-adic group with connected centre. Journal of Noncommutative Geometry, 10 (2), 663-680. (doi:10.4171/JNCG/244).

Record type: Article

Abstract

Let G be a split reductive p-adic group with connected centre.
We show that each Bernstein block in the principal series of G admits a definite geometric structure, namely that of an extended quotient. For the Iwahori-spherical block, this extended quotient has the form T//W where T is a maximal torus in the Langlands dual group of G and W is the Weyl group of G.

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Accepted/In Press date: 22 July 2015
Published date: 1 July 2016
Keywords: reductive p-adic group, representation theory, geometric structure, local langlands conjecture
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 380414
URI: https://eprints.soton.ac.uk/id/eprint/380414
ISSN: 1661-6952
PURE UUID: 9a682261-c708-4279-bb3c-7e514b97d634

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Date deposited: 14 Sep 2015 13:19
Last modified: 19 Jul 2019 20:36

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Contributors

Author: Anne-Marie Aubert
Author: Paul Baum
Author: Roger Plymen
Author: Maarten Solleveld

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