Abstract
A representation of the quantum affine algebra\(U_q (\widehat{sl}_3 )\) of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq → 1 limit. The analogues of the screening currents are also obtained. They commute with the action of\(U_q (\widehat{sl}_3 )\) modulo total differences of some fields.
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Davies B., Foda O., Jimbo M., Miwa T., and Nakayashiki A., Diagonalization of the XXZ Hamiltonian by vertex operators,Comm. Math. Phys. 151, 89–154 (1993).
Frenkel, I. B. and Reshetikhin, N. Yu., Quantum affine algebras and holonomic difference equations,Comm. Math. Phys. 146, 1–60 (1992).
Jimbo, M., Miki, K., Miwa, T., and Nakayashiki, A., correlation functions of the XXZ model for Δ < - 1,Phys. Lett. A168, 256–263 (1992).
Frenkel, I. B. and Jing, N. H., Vertex representations of quantum affine algebras,Proc. Nat'l. Acad. Sci. USA 85, 9373–9377 (1988).
Idzumi, M., Iohara, K., Jimbo, M., Miwa, T., Nakashima, T., and Tokihiro, T., Quantum affine symmetry in vertex models,Internat. J. Modern Phys. A8, 1479–1511 (1993).
Shiraishi, J., Free boson representation of\(U_q (\widehat{sl}_2 )\),Phys. Lett. A 171, 243–248 (1992); Kato, A., Quano, Y-H., and Shiraishi, J., Free boson representation ofq-vertex operators and their correlation functions, to appear inComm. Math. Phys.
Matsuo, A., Free field realization of quantum affine algebra\(U_q (\widehat{sl}_2 )\), Preprint Nagoya Univ. (1992); Free field realization ofq-deformed primary fields for\(U_q (\widehat{sl}_2 )\), Preprint Nagoya Univ. (1992). Abada, A., Bougourzi, A. H., and El Gradechi, M. A., Deformation of the Wakimoto construction, Preprint (1992); Kimura, K., On free boson representation of the quantum affine algebra\(U_q (\widehat{sl}_2 )\), Preprint RIMS-910 (1992).
Drinfeld, V. G., A new realization of Yangians and quantum affine algebras,Soviet Math. Doklady 36, 212–216 (1988).
Wakimoto, M., Fock representations of the affine Lie algebraA (1)1 Comm. Math. Phys. 104, 605–609 (1986); Bershadsky, M. and Ooguri, H., Hidden SL(n) symmetry in conformal field theories,Comm. Math. Phys. 126, 49-83 (1989).
Friedan, D., Martinec, E., and Shenker, S., Conformal invariance, supersymmetry and string theory,Nuclear Phys. B271, 93–165 (1986).
Feigin, B. L. and Frenkel, E. V., Affine Kac-Moody algebras and semi-infinite flag manifolds,Comm. Math. Phys. 128, 161–189 (1990); Ito, K. and Kazama, Y., Feigin-Fuchs representation ofA (1) n affine Lie algebra and the associated parafermionic algebra,Modern Phys. Lett A5, 215-224 (1990); Kuwahara, M. and Suzuki, H., Coset conformal models ofW-algebra and their Feigin-Fuchs construction,Phys. Lett. B 235, 52–56 (1990).
Awata, H., Noumi, M., and Odake, S., Heisenberg realization for\(U_q (\widehat{sl}_n )\) on the flag manifold, Preprint YITP/K-1016 (1993).
Matsuo, A., Jackson integrals of Jordan-Pochhammer type and Knizhnik-Zamolodchikov equations, Preprint Nagoya Univ. (1992); Quantum algebra structure of certain Jackson integrals, Preprint Nagoya Univ. (1992).
Reshetikhin, N., Jackson-type integrals, bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system,Lett. Math. Phys. 26, 153 (1992).
Awata, H., Odake, S., and Shiraishi, J., in preparation.
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On leave from Department of Physics, University of Tokyo, Tokyo 113, Japan.