Conjectures about p-adic groups and their non commutative geometry

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

    Research output: Contribution to journalArticlepeer-review

    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 forG, 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
    Pages (from-to)15-51
    JournalContemporary Mathematics
    Volume691
    Publication statusPublished - 1 Jan 2017

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