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

@article{Kojima2021QuadraticRO,
title={Quadratic relations of the deformed W-superalgebra Wq,tA(M,N)},
author={Takeo Kojima},
journal={Journal of Physics A: Mathematical and Theoretical},
year={2021},
volume={54}
}
• T. Kojima
• Published 27 December 2020
• Mathematics
• Journal of Physics A: Mathematical and Theoretical
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 construction, we introduce the higher W-currents and obtain a closed set of quadratic relations among them. These relations are independent of the choice of Dynkin diagrams for the Lie superalgebra A(M, N), though the screening currents are not. This allows us to define Wq,tA(M,N) by generators and…
4 Citations

### 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

### A note on quiver quantum toroidal algebra

• Mathematics
Journal of High Energy Physics
• 2022
Abstract Recently, Li and Yamazaki proposed a new class of infinite-dimensional algebras, quiver Yangian, which generalizes the affine Yangian $$\mathfrak{gl}$$ gl 1. The characteristic feature

### Shifted quiver quantum toroidal algebra and subcrystal representations

• Mathematics
Journal of High Energy Physics
• 2022
Abstract Recently, new classes of infinite-dimensional algebras, quiver Yangian (QY) and shifted QY, were introduced, and they act on BPS states for non-compact toric Calabi-Yau threefolds. In

### 5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$

We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition

## References

SHOWING 1-10 OF 27 REFERENCES

### The Integrals of Motion for the Deformed W-Algebra Wqt(sl_N^)

• Mathematics
• 2006
We review the deformed W -algebra Wq,t(ŝlN ) and its screening currents. We explicitly construct the Local Integrals of Motion In (n = 1, 2, · · ·) for this deformed W -algebra. We explicitly

### 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

### 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

### 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

### Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1

• Mathematics
• 1995
Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which areq-deformations of the classicalW. We also define their free field realizations, i.e. homomorphisms

### The Integrals of Motion for the Deformed W-Algebra $${W_{q,t}(\widehat{gl_N})}$$. II. Proof of the Commutation Relations

• Mathematics
• 2008
We explicitly construct two classes of infinitely many commutative operators in terms of the deformed W-algebra $${W_{q,t}(\widehat{gl_N})}$$, and give proofs of the commutation relations of these

### A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

• Mathematics
• 1996
A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra.

### 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

### 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