Affine Grassmannians and Geometric Satake Equivalences

Abstract

I extend the ramified geometric Satake equivalence of Zhu from tamely ramified groups to include the case of general connected reductive groups. As a prerequisite I prove basic results on the geometry of affine flag varieties.

arXiv commentIn the new version, I added Appendices A and B to supplement some proofs in the main body of the manuscript. Especially, Lemma 2.1 is new which concerns the extension of some group schemes over complete DVRs in equal characteristic to some pointed curve