  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.
