On the geometric Satake equivalence for Kac-Moody groups

2025/10/13 by Bouthier, Alexis, Vasserot, Eric
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.11466

Abstract

This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double affine grassmannian \Gr_G, seen as a infty-stack, that we equip with a t-structure. We obtain an Braden's hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact using dimension estimates for affine MV-cycles. We then deduce the sought-for equivalence and prove that the IC-complexes match with the irreducible highest weight representations of the Langlands dual group G^\vee.

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