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arxiv: math/0107215 · v3 · submitted 2001-07-30 · 🧮 math.QA · math.RT

Drinfeld-Sokolov reduction for quantum groups and deformations of W-algebras

A. Sevostyanov This is my paper
classification 🧮 math.QA math.RT
keywords q-algdeformedquantumgroupsscreeningw-algebrasaffinealgebra
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We define deformations of W-algebras associated to complex semi-simple Lie algebras by means of quantum Drinfeld-Sokolov reduction procedure for affine quantum groups. We also introduce Wakimoto modules for arbitrary affine quantum groups and construct free field resolutions and screening operators for the deformed W-algebras. We compare our results with earlier definitions of q-W-algebras and of the deformed screening operators due to Awata, Kubo, Odake, Shiraishi (q-alg/9507034, q-alg/9508011, q-alg/9612001), Feigin, E. Frenkel (q-alg/9508009) and E. Frenkel, Reshetikhin (q-alg/9708006). The screening operator and the free field resolution for the deformed W-algebra associated to the simple Lie algebra sl(2) coincide with those for the deformed Virasoro algebra introduced in q-alg/9507034.

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

    math.QA 2026-06 unverdicted novelty 6.0

    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.