Parabolic induction and Hecke modules in characteristic p for p-adic GLn

Ollivier, Rachel

doi:10.2140/ant.2010.4.701

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Parabolic induction and Hecke modules in characteristic $p$ for $p$-adic GL$_n$

Rachel Ollivier

Vol. 4 (2010), No. 6, 701–742

DOI: 10.2140/ant.2010.4.701

Abstract

We classify the simple supersingular modules for the pro- $p$ -Iwahori Hecke algebra $ℋ$ of $p$ -adic ${G L}_{n}$ by proving a conjecture by Vignéras about a mod $p$ numerical Langlands correspondence on the side of the Hecke modules. We define a process of induction for $ℋ$ -modules in characteristic $p$ that reflects the parabolic induction for representations of the $p$ -adic general linear group and explore the semisimplification of the standard nonsupersingular $ℋ$ -modules in light of this process.

Keywords

mod $p$ representations of Hecke algebras and $p$-adic groups, parabolic induction, integral Bernstein presentation, integral Satake transform

Mathematical Subject Classification 2000

Primary: 20C08

Secondary: 20G05, 22E50

Milestones

Received: 2 July 2009

Revised: 21 April 2010

Accepted: 6 June 2010

Published: 25 September 2010

Authors

Rachel Ollivier
Université de Versailles Saint-Quentin Laboratoire de Mathématiques de Versailles 45 avenue des États-Unis 78035 Versailles Cedex France	Columbia University Mathematics Department MC 4445 2990 Broadway New York, NY 10027 United States

Vol. 4, No. 6, 2010