Vol. 8, No. 5, 2014

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Compatibility between Satake and Bernstein isomorphisms in characteristic $p$

Rachel Ollivier

Vol. 8 (2014), No. 5, 1071–1111
Abstract

We study the center of the pro-p Iwahori–Hecke ring H̃ of a connected split p-adic reductive group G. For k an algebraically closed field of characteristic p, we prove that the center of the k-algebra H̃ k contains an affine semigroup algebra which is naturally isomorphic to the Hecke k-algebra (G,ρ) attached to an irreducible smooth k-representation ρ of a given hyperspecial maximal compact subgroup of G. This isomorphism is obtained using the inverse Satake isomorphism defined in our previous work.

We apply this to classify the simple supersingular H̃ k-modules, study the supersingular block in the category of finite-length H̃ k-modules, and relate the latter to supersingular representations of G.

Keywords
Hecke algebras, characteristic $p$, Satake isomorphism, supersingularity
Mathematical Subject Classification 2010
Primary: 20C08
Secondary: 22E50
Milestones
Received: 25 April 2013
Revised: 27 December 2013
Accepted: 27 February 2014
Published: 16 September 2014
Authors
Rachel Ollivier
Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027
United States