Work

Conjectures about p-adic groups and their noncommutative geometry

Year: 2015

Type: preprint

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.

Source: MIMS EPrints (University of Southampton)

DOI: 10.48550/arxiv.1508.02837

Authors: Aubert, Anne-Marie, Baum, Paul, Plymen, Roger, Solleveld, Maarten

Institutions: Institut de Mathématiques de Jussieu-Paris Rive Gauche, University of Manchester, University of Southampton, Radboud University Nijmegen

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2256767199

Cites: 22

Cited by: 5

Related to: 20