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

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

1997-02-11

arxiv.org/abs/q-alg/9702016v4

Mathematics

Quantum Algebra

19 pp., AMS-LaTeX. The paper replaces a temporarily withdrawn text; the first part (written by E. Frenkel, N. Reshetikhin, and

Scientific paper

10.1007/s002200050312

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.

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