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

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2015) Geometric structure for the principal series of a split reductive p-adic group with connected centre. [MIMS Preprint]

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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.

Item Type: MIMS Preprint
Additional Information: J. Noncommutative Geometry, to appear
Uncontrolled Keywords: Reductive p-adic group, extended quotient, geometric structure, Langlands dual group
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
MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups
Depositing User: Professor Roger Plymen
Date Deposited: 15 Aug 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2367

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