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2012.109: Geometric structure and the local Langlands conjecture

2012.109: Anne-Marie Aubert, Paul Baum, Roger Plymen and Maarten Solleveld (2012) Geometric structure and the local Langlands conjecture.

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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 2000 > 11 Number theory
MSC 2000 > 20 Group theory and generalizations
MSC 2000 > 22 Topological groups, Lie groups
MIMS number:2012.109
Deposited By:Professor Roger Plymen
Deposited On:02 December 2012

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