Geometric structure and the local Langlands conjecture

Aubert, Anne-Marie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2012) Geometric structure and the local Langlands conjecture. [MIMS Preprint]

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Abstract

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric structure, in both the smooth dual and the Langlands parameters. We prove that this geometric structure is present, in the same way, for the general linear group, including all of its inner forms. With these results as evidence, we give a detailed formulation of a general geometric structure conjecture.

Item Type: MIMS Preprint
Uncontrolled Keywords: Representation theory, geometric structure, local Langlands conjecture, reductive p-adic 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: 02 Dec 2012
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1918

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