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arXiv · 2112.06747

Satake equivalence for Hodge modules on affine Grassmannians

Roman Fedorov
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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.

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Roman Fedorov. 2021-12-13. Satake equivalence for Hodge modules on affine Grassmannians. https://arxiv.org/abs/2112.06747

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