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 \(\check G\) 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 \(\check G\) in terms of the geometry of \(Gr_G\). The idea of the construction belongs to Jacob Lurie.