Abstract
Primary fields of the q-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields are represented by the shift operator Θξf(x) = f(ξx). Four point functions of the primary fields enjoy the connection formula associated with the Boltzmann weights of the fusion Andrews–Baxter–Forrester model.
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References
Belavin, A. A., Polyakov, A. M. and Zamolodchikov, A. B.: Nuclear Phys. B 241 (1984), 333; Itzykson, C., Saleur, H. and Zuber, J.-B. (eds): Conformal Invariance and Applications in Statistical Mechanics, World Scientific, Singapore, 1988.
Andrews, G. E., Baxter, R. J. and Forrester, P. J.: Eight-vertex SOS model and generalized Rogers-Ramnujan identities, J. Statist. Phys. 35 (1984), 193-266, Date, E., Jimbo, M., Kuniba, A., Miwa, T. and Okado, M.: Exactly solvable SOS models: Local height probabilities and theta function identities, Nuclear Phys. B 290 (1987), 231-273; Exactly solvable SOSmodels 2: Proof of the star-triangle relation and combinatorial identities. Adv. Stud. Pure. Math. 16 (1988), 17-122, Jimbo, M.: Yang-Baxter Equation in Integrable Systems World Scientific, Singapore, 1989
Lukyanov, S. and Pugai, Y.: Bosonization of ZF algebras: Direction toward deformed Virasoro algebra, hepth/9412128.
Shiraishi, J., Kubo, H., Awata, H. and Odake, S.: A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions, Lett. Math. Phys. 38 (1996), 33-51.
Awata, H., Kubo, H., Odake, S. and Shiraishi, J.: Quantum WN algebras and Macdonald polynomials, Comm. Math. Phys. 179 (1996), 401-416.
Feigin, B. and Frenkel, B.: Quantum W-algebras and elliptic algebras, Comm. Math. Phys. 178 (1996), 653-678.
Lukyanov, S.: A note on the deformed Virasoro algebra, Phys. Lett. B 367 (1996), 121-125.
Lukyanov, S. and Pugai, Y.:Multi-point local height probabilities in the integrable RSOSModel, Nuclear Phys. B 473 (1996), 631-658.
Kadeishvili, A. A.: Vertex operators for deformed Virasoro algebra, hepth/9604153.
Asai, Y., Jimbo, M., Miwa, T. and Pugai, Y.: Bosonization of vertex operators for the A(1)n–1 face model, hep-th/9606095.
Gasper, G. and Rahman, M.: Basic Hypergeometric Series, Cambridge University Press, 1990.
Felder, G.: BRST approach to minimal models, Nuclear Phys. B 317 (1989), 215.
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AWATA, H., KUBO, H., MORITA, Y. et al. Vertex Operators of the q-Virasoro Algebra; Defining Relations, Adjoint Actions and Four Point Functions. Letters in Mathematical Physics 41, 65–78 (1997). https://doi.org/10.1023/A:1007321109584
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DOI: https://doi.org/10.1023/A:1007321109584