# Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators

@article{Ding1998QuantizedWO,
title={Quantized W-algebra of sl(2,1) : a construction from the quantization of screening operators},
author={Jintai Ding and Boris Feigin},
journal={arXiv: Quantum Algebra},
year={1998}
}
• Published 19 January 1998
• Mathematics
• arXiv: Quantum Algebra
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 the form of a sum of two vertex operators which has the simplest correlation functions with the quantized screen operator, namely a function with one pole and one zero, then, the screen operator and this operator are uniquely determined, and this operator is the quantized virasoro algebra. For the…

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## References

SHOWING 1-10 OF 22 REFERENCES

### Integrals of motion and quantum groups

• Mathematics
• 1993
A homological construction of integrals of motion of the classical and quantum Toda field theories is given. Using this construction, we identify the integrals of motion with cohomology classes of

### 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

### 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

### Difference equations of quantum current operators and quantum parafermion construction

• Mathematics, Physics
• 1996
For the current realization of the affine quantum groups, a simple comultiplication for the quantum current operators was given by Drinfeld. With this comultiplication, we prove that, for the

### 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.

### Exactly solved models in statistical mechanics

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical

### Integral representations of the Macdonald symmetric polynomials

• Mathematics
• 1996
Multiple-integral representations of the (skew-)Macdonald symmetric polynomials are obtained. Some bosonization schemes for the integral representations are also constructed.

• Phys. 318
• 1989

### Phys

• Lett. A171 (1992) 243-248; H. Awata, S. Odake, J. Shiraishi, Comm. Math. Phys. 162
• 1994

### Comm

• Math. Phys. 131
• 1990