Rachel Ollivier
Published 2012-11-22, updated 2014-08-15Version 2
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.
Comments: The new version contains the classification of the simple supersingular Hecke modules in the case of a general split group
On the exactness of ordinary parts over a local field of characteristic $p$
An inverse Satake isomorphism in characteristic p
Inductive AM condition for the alternating groups in characteristic 2
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