MIT Lie Groups Seminar

Building 2, 2-142

Speaker: Simon Riche (Université Clermont Auvergne)Title: A modular ramified Satake equivalenceAbstract: The geometric Satake equivalence is a celebrated construction (with contributions by Lusztig, Ginzburg, Drinfeld and Mirkovic-Vilonen) that realizes the category of representations of a connected reductive group as a category of perverse sheaves on the affine Grassmannian of the Langlands dual group. In the setting of l-adic coefficients, Zhu and Richarz have studied a variant of this construction in a "ramified" situation, where the group of which one takes the affine Grassmannian can be a non constant group scheme over formal loops. In this talk I'll explain a version of this equivalence for general coefficients; the Tannakian group on the dual side is then a certain group of fixed points for automorphisms of a reductive group, which is not necessarily smooth. This is joint work with P. Achar, J. Lourenço and T. Richarz.