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arXiv · 2106.12500

A tale of parahoric--Hecke algebras, Bernstein and Satake homomorphisms

Reda Boumasmoud
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Abstract

Let $\mathbf{G}$ be a connected reductive group over a {non-archimedean local field} $F$. Let $K_\mathcal{F}$ be the parahoric subgroup attached to a facet $\mathcal{F}$ in the Bruhat--Tits building of $\mathbf{G}$. The ultimate goal of the present paper is to describe the center of the parahoric--Hecke algebra $\mathcal{H}(\mathbf{G}(F)//K_{\mathcal{F}}, \mathbb{Z}[q^{-1}])$ with level $K_{\mathcal{F}}$ and prove the compatibility of generalized (twisted) Bernstein and Satake homomorphisms.

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Reda Boumasmoud. 2021-06-23. A tale of parahoric--Hecke algebras, Bernstein and Satake homomorphisms. https://arxiv.org/abs/2106.12500

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