Compatibility between Satake and Bernstein-type isomorphisms in characteristic p
Abstract
We study the center of the pro-p Iwahori-Hecke ring H of a connected split p-adic reductive group G. For k an algebraically closed field with characteristic p, we prove that the center of the k-algebra H_k:= H\otimes_Z k contains an affine semigroup algebra which is naturally isomorphic to the Hecke algebra attached to any irreducible smooth k-representation of a given hyperspecial maximal compact subgroup of G. This isomorphism is obtained using the inverse Satake isomorphism constructed in arXiv:1207.5557. We apply this to classify the simple supersingular H_k-modules, study the supersingular block in the category of finite length H_k-modules, and relate the latter to supersingular representations of G.
Cite
@article{arxiv.1211.5366,
title = {Compatibility between Satake and Bernstein-type isomorphisms in characteristic p},
author = {Rachel Ollivier},
journal= {arXiv preprint arXiv:1211.5366},
year = {2016}
}
Comments
The new version contains the classification of the simple supersingular Hecke modules in the case of a general split group