Celebratio Mathematica — Baum — Aubert/Plymen/Solleveld

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Works connected to Alberto Mínguez

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A.-M. Aubert, P. Baum, R. Plymen, and M. Solleveld: “Conjectures about \( p \)-adic groups and their noncommutative geometry,” pp. 15–51 in Around Langlands correspondences (Orsay, France, 17–20 June 2015). Edited by F. Brumley, M. P. Gómez Aparicio, and A. Minguez. Contemporary Mathematics 691. American Mathematical Society (Providence, RI), 2017. MR 3666049 ArXiv 1508.02837 incollection

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.

Farrell Brumley	Related
Alberto Mínguez	Related
Anne-Marie Aubert	Related
Roger J. Plymen	Related
Maarten Solleveld	Related