Geometry Seminar

The geometric Satake equivalence is a cornerstone of geometric representation theory, and of the geometric Langlands program in particular. It relates perverse sheaves on a topological space, the affine Grassmannian, associated to a complex reductive group G, to representations of the Langlands dual group G^\vee. The goal of this talk is to present progress towards a similar equivalence with G replaced by a real reductive group, and to present the full equivalence in the special case of GL(2, R). The most surprising point is that the dual group G^\vee is now a quantum group. I will also explain the relationship of this problem with the relative Langlands program for symmetric spaces.