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 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.