Twisted Whittaker model and factorizable sheaves

Abstract.

Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group Ğ in terms of spherical perverse sheaves (or D-modules) on the affine Grassmannian Gr _G = G((t))/G[[t]] of the original group G. In the present paper we perform a first step in realizing the category of representations of the quantum group corresponding to Ğ in terms of the geometry of Gr _G . The idea of the construction belongs to Jacob Lurie.