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

• Alexei Sevostyanov ^[1]
  1. [1] Department of Mathematics, ETH-Zentrum, Suiza
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 8, Nº. 4, 2002, págs. 637-703
• Idioma: inglés
• DOI: 10.1007/bf02637314
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• Resumen

  • We define deformations of W-algebras associated to comple semisimple 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 [60],[6], [7], Feigin, E. Frenkel [22] and E. Frenkel, Reshetikhin [34]. The screening operator and the free field resolution for the deformed W-algebra associated to the simple Lie algebra sl2 coincide with those for the deformed Virasoro algebra introduced in [60].