Satake equivalence for Hodge modules on affine Grassmannians

Abstract

For a reductive group $G$ we equip the category of $G_{\mathcal{O}}$-equivariant polarizable pure Hodge modules on the affine Grassmannian ${\mathrm{Gr}}_G$ with a structure of neutral Tannakian category. We show that it is equivalent to a twisted tensor product of the category of representations of the Langlands dual group and the category of pure polarizable Hodge structures.

arXiv commentA historical mistake regarding the geometric Satake equivalence is corrected