Conjectures about p-adic groups and their noncommutative geometry

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2015) Conjectures about p-adic groups and their noncommutative geometry. [MIMS Preprint]

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Abstract

Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statements about the geometric structure of Bernstein components for G, both at the level of the space of irreducible representations and at the level of the associated Hecke algebras. We relate this to two well-known conjectures: the local Langlands correspondence and the Baum-Connes conjecture for G. In particular, we present a strategy to reduce the local Langlands correspondence for irreducible G-representations to the local Langlands correspondence for supercuspidal representations of Levi subgroups.

Item Type: MIMS Preprint
Uncontrolled Keywords: Reductive p-adic group, local Langlands correspondence, Baum-Connes, noncommutative geometry
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 19 K-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/2365

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