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2014 Compatibility between Satake and Bernstein isomorphisms in characteristic $p$
Rachel Ollivier
Algebra Number Theory 8(5): 1071-1111 (2014). DOI: 10.2140/ant.2014.8.1071

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 H̃k 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 H̃k-modules, study the supersingular block in the category of finite-length H̃k-modules, and relate the latter to supersingular representations of G.

Citation

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Rachel Ollivier. "Compatibility between Satake and Bernstein isomorphisms in characteristic $p$." Algebra Number Theory 8 (5) 1071 - 1111, 2014. https://doi.org/10.2140/ant.2014.8.1071

Information

Received: 25 April 2013; Revised: 27 December 2013; Accepted: 27 February 2014; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1329.22010
MathSciNet: MR3263136
Digital Object Identifier: 10.2140/ant.2014.8.1071

Subjects:
Primary: 20C08
Secondary: 22E50

Rights: Copyright © 2014 Mathematical Sciences Publishers

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