Towards Drinfeld-Sokolov reduction for quantum groups

In this paper we study the Poisson-Lie version of the Drinfeld-Sokolov reduction defined in q-alg/9704011, q-alg/9702016. Using the bialgebra structure related to the new Drinfeld realization of affine quantum groups we describe reduction in terms of constraints. This realization of reduction admits direct quantization. As a byproduct we obtain an explicit expression for the symplectic form associated to the twisted Heisenberg double and calculate the moment map for the twisted dressing action. For some class of infinite-dimensional Poisson Lie groups we also prove an analogue of the Ginzburg-Weinstein isomorphism.