DRINFELD-SOKOLOV REDUCTION FOR DIFFERENCE-OPERATORS AND DEFORMATIONS OF W-ALGEBRAS - II - THE GENERAL SEMISIMPLE CASE

The paper is the sequel to [9]. We extend the Drinfeld-Sokolov reducti on procedure to q-difference operators associated with arbitrary semis imple Lie algebras. This leads to a new elliptic deformation of the Li e bialgebra structure on the associated loop algebra. The related clas sical r-matrix is explicitly described in terms of the Coxeter transfo rmation. We also present a cross-section theorem for q-gauge transform ations which generalizes a theorem due to R. Steinberg.