Twisted Whittaker model and factorizable sheaves

Let G be a reductive group. The geometric Satake equivalence realized the category of representations of the Langlands dual group G 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 G in terms of the geometry of Gr(G). The idea of the construction belongs to Jacob Lurie.