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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Received: 27 April 1997 / Accepted: 22 August 1997
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Semenov-Tian-Shansky, M., Sevostyanov, A. Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case . Comm Math Phys 192, 631–647 (1998). https://doi.org/10.1007/s002200050312
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DOI: https://doi.org/10.1007/s002200050312