# 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} }

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

- Physics
- 1982

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.

### Nucl

- 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