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

Reda Boumasmoud

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 Bru…