Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case

@article{SemenovTianShansky1998DrinfeldSokolovRF,
  title={Drinfeld–Sokolov Reduction for Difference
Operators and Deformations of W-Algebras¶ II. The General Semisimple Case
},
  author={Michael Arsen'evich Semenov-Tian-Shansky and A. V. Sevostyanov},
  journal={Communications in Mathematical Physics},
  year={1998},
  volume={192},
  pages={631-647}
}
Abstract:The paper is the sequel to [9]. 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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