Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case

Abstract

The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic deformation of the Lie bialgebra structure on the associated loop algebra. The related classical r-matrix is explicitly described in terms of the Coxeter transformation. We also present a cross-section theorem for q-gauge transformations which generalizes a theorem due to R.Steinberg.

19 pp., AMS-LaTeX. The paper replaces a temporarily withdrawn text; the first part (written by E. Frenkel, N. Reshetikhin, and M. A. Semenov-Tian-Shansky) is available as q-alg/9704011

References in corpus (1)

• Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra

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