2001/07/30 by A. Sevostyanov, Sevostyanov, A.
Mathematics · #17B37 (Primary) #20C08 (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:20C08
paper · pdf · doi:10.48550/arxiv.math/0107215
55 pages, AMSLaTeX, misprints corrected, the list of references extended, minor changes in the exposition
openalex publication_date 2001/07/30 · arxiv created 2002/05/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.