# 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…

## 10 Citations

### BRST Operator for Quantum Lie Algebras: Relation to the Bar Complex

- Mathematics
- 2004

Quantum Lie algebras (an important class of quadratic algebras arising in the Woronowicz calculus on quantum groups) are generalizations of Lie (super)algebras. Many notions from the theory of Lie…

### Quadratic relations of the deformed W-algebra for the twisted affine algebra A ( 2 ) 2

- Mathematics
- 2021

We revisit the free field construction of the deformed W -algebra by Frenkel and Reshetikhin, Commun. Math. Phys. 197, 1-31 (1998), where the basic W -current has been identified. Herein, we…

### Quadratic relations of the deformed $W$-algebra for the twisted affine algebra of type $A_{2N}^{(2)}$

- Mathematics
- 2021

. We revisit the free ﬁeld construction of the deformed W -algebra by Frenkel and Reshetikhin, Commun. Math. Phys. 197 , 1-31 (1998), where the basic W -current has been identiﬁed. Herein, we…

### Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))

- Mathematics
- 2019

This paper is a continuation of study by J.Ding and B.Feigin. We find a bosonization of the deformed $W$-superalgebras ${\cal W}_{q t}(\mathfrak{sl}(2|1))$ that commutes up-to total difference with…

### Quadratic relations of the deformed W-superalgebra Wq,tA(M,N)

- Mathematics
- 2021

We find the free field construction of the basic W-current and screening currents for the deformed W-superalgebra Wq,tA(M,N) associated with Lie superalgebra of type A(M, N). Using this free field…

### Quadratic relations of the deformed W-superalgebra

- Mathematics
- 2020

This paper is a continuation of the study by Ding and Feigin, Contemp.Math. 248, 83 (1998). We find a bosonization of the deformed W -superalgebras Wq,t(sl(2|1)) that commute up to the total…

### Multiplicative Hitchin systems and supersymmetric gauge theory

- MathematicsSelecta Mathematica
- 2019

Multiplicative Hitchin systems are analogues of Hitchin's integrable system based on moduli spaces of G-Higgs bundles on a curve C where the Higgs field is group-valued, rather than Lie algebra…

### D ec 2 02 0 Quadratic relations of the deformed W-superalgebra

- Mathematics, Physics
- 2021

We find the free field construction of the basic W -current and screening currents for the deformed W -superalgebra Wq,t (

### A pr 2 02 1 Quadratic relations of the deformed

- 2021

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