Vol. 4, No. 2, 2022

Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN (electronic): 2576-7666
ISSN (print): 2576-7658
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Representations of a reductive $p$-adic group in characteristic distinct from $p$

Guy Henniart and Marie-France Vignéras

Vol. 4 (2022), No. 2, 249–305
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 ind JGλ 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 ind JGλ, 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 ind JGλ is supercuspidal if and only if λ is supercuspidal.

PDF Access Denied

We have not been able to recognize your IP address 3.238.72.180 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
modular representations of reductive $p$-adic groups, cuspidal types, supercuspidal modular representations
Mathematical Subject Classification
Primary: 11F55, 22E50
Milestones
Received: 16 November 2020
Revised: 14 August 2021
Accepted: 31 August 2021
Published: 24 August 2022
Authors
Guy Henniart
Laboratoire de Mathématiques d’Orsay
Univ. Paris–Sud
Orsay
France
Marie-France Vignéras
Institut de Mathématiques de Jussieu–Paris Rive Gauche
Université de Paris 7
Paris
France