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

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arxiv q-alg/9702016 v4 pith:YP6X65OH submitted 1997-02-11 q-alg math.QA

M. A. Semenov-Tian-Shansky , A.V. Sevostyanov This is my paper · ORCID
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. $Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory

    hep-th 2025-07 conditional novelty 7.0 of 10

    In 5d N=1 U(N) gauge theory, codimension-two defects produce Q-operators whose q-difference equations are the Baxter TQ equations of XXZ spin chains built on bi-infinite evaluation modules of quantum affine algebras.

  2. Deformed W-algebras and chiralized cluster seeds: subregular W-algebras and Inverse Quantum Hamiltonian Reduction

    math.QA 2026-06 unverdicted novelty 6.0 of 10

    Applies chiral cluster seeds to deformed W-algebras, introduces W_{q,t}^sub(sl(N)), and constructs embeddings viewed as deformed inverse quantum Hamiltonian reduction.

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