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

@article{Sevostyanov2001DrinfeldSokolovRF,
title={Drinfeld–Sokolov reduction for quantum groups and deformations of W-algebras
},
author={A. V. Sevostyanov},
journal={Selecta Mathematica},
year={2001},
volume={8},
pages={637-703}
}
Abstract. We define deformations of W-algebras associated to complex 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…

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