Vol. 4, No. 6, 2010

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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
Abstract

We classify the simple supersingular modules for the pro-p-Iwahori Hecke algebra of p-adic GLn 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 -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 -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