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2022 Representations of a reductive p-adic group in characteristic distinct from p
Guy Henniart, Marie-France Vignéras
Tunisian J. Math. 4(2): 249-305 (2022). DOI: 10.2140/tunis.2022.4.249

Abstract

We investigate the irreducible cuspidal C-representations of a reductive p-adic group G over a field C of characteristic different from p. In all known cases, such a representation is the compactly induced representation indJGλ from a smooth C-representation λ of a compact modulo centre subgroup J of G. When C is algebraically closed, for many groups G, a list of pairs (J,λ) has been produced, such that any irreducible cuspidal C-representation of G has the form indJGλ, for a pair (J,λ) unique up to conjugation. We verify that those lists are stable under the action of field automorphisms of C, and we produce similar lists when C is no longer assumed algebraically closed. Our other main result concerns supercuspidality. This notion makes sense for the irreducible cuspidal C-representations of G, but also for the representations λ above, which involve representations of finite reductive groups. In most cases we prove that indJGλ is supercuspidal if and only if λ is supercuspidal.

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Guy Henniart. Marie-France Vignéras. "Representations of a reductive p-adic group in characteristic distinct from p." Tunisian J. Math. 4 (2) 249 - 305, 2022. https://doi.org/10.2140/tunis.2022.4.249

Information

Received: 16 November 2020; Revised: 14 August 2021; Accepted: 31 August 2021; Published: 2022
First available in Project Euclid: 2 September 2022

Digital Object Identifier: 10.2140/tunis.2022.4.249

Subjects:
Primary: 11F55 , 22E50

Keywords: cuspidal types , modular representations of reductive p-adic groups , supercuspidal modular representations

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2022
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