Conjectures about p-adic groups and their noncommutative geometry

Anne Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)

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.

Original languageEnglish (US)
Title of host publicationContemporary Mathematics
PublisherAmerican Mathematical Society
Pages15-51
Number of pages37
DOIs
StatePublished - Jan 1 2017

Publication series

NameContemporary Mathematics
Volume691
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

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P-adic Groups
Noncommutative Geometry
Correspondence
Baum-Connes Conjecture
Hecke Algebra
Reductive Group
Geometric Structure
Representation Theory
Irreducible Representation
Subgroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Aubert, A. M., Baum, P., Plymen, R., & Solleveld, M. (2017). Conjectures about p-adic groups and their noncommutative geometry. In Contemporary Mathematics (pp. 15-51). (Contemporary Mathematics; Vol. 691). American Mathematical Society. https://doi.org/10.1090/conm/691/13892
Aubert, Anne Marie ; Baum, Paul ; Plymen, Roger ; Solleveld, Maarten. / Conjectures about p-adic groups and their noncommutative geometry. Contemporary Mathematics. American Mathematical Society, 2017. pp. 15-51 (Contemporary Mathematics).
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Aubert, AM, Baum, P, Plymen, R & Solleveld, M 2017, Conjectures about p-adic groups and their noncommutative geometry. in Contemporary Mathematics. Contemporary Mathematics, vol. 691, American Mathematical Society, pp. 15-51. https://doi.org/10.1090/conm/691/13892

Conjectures about p-adic groups and their noncommutative geometry. / Aubert, Anne Marie; Baum, Paul; Plymen, Roger; Solleveld, Maarten.

Contemporary Mathematics. American Mathematical Society, 2017. p. 15-51 (Contemporary Mathematics; Vol. 691).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Aubert AM, Baum P, Plymen R, Solleveld M. Conjectures about p-adic groups and their noncommutative geometry. In Contemporary Mathematics. American Mathematical Society. 2017. p. 15-51. (Contemporary Mathematics). https://doi.org/10.1090/conm/691/13892