Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case
q-alg
2009-10-30 v4 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.q-alg/9702016,
title = {Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case},
author = {M. A. Semenov-Tian-Shansky and A. V. Sevostyanov},
journal= {arXiv preprint arXiv:q-alg/9702016},
year = {2009}
}
Comments
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 The paper replaces a temporarily withdrawn text; the first part (written by E. Frenkel, N. Reshetikhin, and M. A. Semenov-Tian-Shansky) is available as q-alg/9704011