• Corpus ID: 237364098

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

@inproceedings{Kojima2021QuadraticRO,
title={Quadratic relations of the deformed \$W\$-algebra for the twisted affine algebra \$A\_\{2N\}^\{(2)\}\$},
author={Takeo Kojima},
year={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 establish a free field construction of higher W -currents of the deformed W -algebra associated with the twisted affine algebra A (2) 2N . We obtained a closed set of quadratic relations and duality, which allowed us to define the deformed W -algebra Wx,r (

## References

SHOWING 1-10 OF 19 REFERENCES
Deformations of W-algebras associated to simple Lie algebras
• Mathematics
• 1997
Deformed W-algebra Wq,t(g) associated to an arbitrary simple Lie alge- bra g is defined together with its free field realizations and the screening operators. Explicit formulas are given for
Quadratic relations of the deformed W-superalgebra Wq,t(sl(2|1))
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
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
Drinfeld–Sokolov reduction for quantum groups and deformations of W-algebras
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
Quantum-algebras and elliptic algebras
• Mathematics
• 1995
AbstractWe define a quantum-algebra associated to $$\mathfrak{s}\mathfrak{l}_N$$ as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes
Quantized W-algebra of sl(2,1) and quantum parafermions of U_q(sl(2))
• Mathematics
• 1998
In this paper, we establish the connection between the quantized W-algebra of ${\frak sl}(2,1)$ and quantum parafermions of $U_q(\hat {\frak sl}(2))$ that a shifted product of the two quantum
Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case
• Mathematics
• 1998
Abstract:The paper is the sequel to [9]. We extend the Drinfeld--Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic
Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra
• Mathematics
• 1998
Abstract:We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in
q-deformation of corner vertex operator algebras by Miura transformation
• Mathematics
• 2021
Recently, Gaiotto and Rapcak proposed a generalization of WN algebra by considering the symmetry at the corner of the brane intersection (corner vertex operator algebra). The algebra, denoted as
Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators
• Mathematics
• 1998
Starting from bosonization, we study the operator that commute or commute up-to a total difference with of any quantized screen operator of a free field. We show that if there exists a operator in