Twisted Whittaker models for metaplectic groups

Let G be a reductive group (over an algebraically closed field) equipped with the metaplectic data. In this paper we study the corresponding twisted Whittaker category for G. We construct and study a functor from the latter category to the corresponding category of factorizable sheaves. It plays the role of the restriction functor from the category of representations of the big quantum group to those of the graded small quantum group. We also prove an analog in our setting of the Lusztig-Steinberg tensor product theorem for quantum groups describing the semi-simple part of the Whittaker category as a module over the Hecke algebra.