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

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

2001-07-30

arxiv.org/abs/math/0107215v3

Mathematics

Quantum Algebra

55 pages, AMSLaTeX, misprints corrected, the list of references extended, minor changes in the exposition

Scientific paper

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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