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arXiv · 2602.02209

Pro-p Iwahori Hecke algebras and the dual Vinberg monoid

Tobias Schmidt
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Abstract

Let G be a split reductive group over the integers, F a p-adic local field with residue field Fq. We relate the pro-p-Iwahori Hecke algebra H of G(F) over Fq to the Vinberg monoid of the dual group and study this relation. As an application, in the GL(n)-case and for F/Qp unramified, we derive a parametrization of SpecZ by semisimple n-dimensional representations of the absolute Galois group of F, generalizing the known case n = 2. Here Z denotes the center of H.

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Tobias Schmidt. 2026-02-02. Pro-p Iwahori Hecke algebras and the dual Vinberg monoid. https://arxiv.org/abs/2602.02209

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