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Free boson representation ofq-vertex operators and their correlation functions

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Abstract

A bosonization scheme of theq-vertex operators of Uq(sl2) for arbitrary level is obtained. They act as intertwiners among the highest weight modules constructed in a bosonic Fock space. An integral formula is proposed forN-point functions and explicit calculation for two-point function is presented.

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References

  1. Itzykson, C., Saleur, H., Zuber, J.-B. (eds.): Conformal Invariance and Applications to Statistical Mechanics. Singapore: World Scientific 1988

    Google Scholar 

  2. Frenkel, I.B., Reshetikhin, N.Yu.: Quantum Affine Algebras and Holonomic Difference Equations. Commun. Math. Phys.146, 1–60 (1992)

    Google Scholar 

  3. Andrews, G.E., Baxter, R.J., Forrester, P.J.: Eight-Vertex SOS Model and Generalized Rogers-Ramanujan-Type Identities. J. Stat. Phys.35, 193–266 (1984)

    Google Scholar 

  4. Jimbo, M., Miwa, T., Okado, M.: Solvable Lattice Models Related to the Vector Representation of Classical Simple Lie Algebras. Commun. Math. Phys.116, 507–525 (1988)

    Google Scholar 

  5. Davies, B., Foda, O., Jimbo, M., Miwa, T., Nakayashiki, A.: Diagonalization of the XXZ Hamiltonian by Vertex Operators. RIMS preprint873 (1992)

  6. Jimbo, M., Miki, K., Miwa, T., Nakayashiki, A.: Correlation Functions of the XXZ model for Δ<−1. RIMS preprint877 (1992)

  7. Frenkel, I.B., Jing, N.H.: Vertex Representations of Quantum Affine Algebras. Proc. Nat'l. Acad. Sci. USA85, 9373–9377 (1988)

    Google Scholar 

  8. Shiraishi, J.: Free Boson Representation of Uq(sl2). Univ. Tokyo preprintUT-617 (1992)

  9. Wakimoto, M.: Fock Representations of the Affine Lie AlgebraA (1)1 . Commun. Math. Phys.104, 605–609 (1986)

    Google Scholar 

  10. Idzumi, M., Iohara, K., Jimbo, M., Miwa, T., Nakashima, T., Tokihiro, T.: Quantum Affine Symmetry in Vertex Models. RIMS preprint (1992)

  11. Drinfeld, V.G.: A New Realization of Yangians and Quantum Affine Algebas. Soviet Math. Doklady36, 212–216 (1988)

    Google Scholar 

  12. Kac, V.G.: Infinite Dimensional Lie Algebras. 3rd ed., Cambridge: Cambridge Univ. Press 1990

    Google Scholar 

  13. Drinfeld, V.G.: Quantum Groups. Proceedings of ICM, Berkeley, 1986, pp. 798–820

  14. Jimbo, M.: Aq-Difference Analogue ofU(g) and the Yang-Baxter Equation. Lett. Math. Phys.10, 63–69 (1985)

    Google Scholar 

  15. Kashiwara, M.: On Crystal Bases of theq-analog of the Universal Enveloping Algebra. Duke Math. J.63, 465–516 (1991)

    Google Scholar 

  16. Date, E., Jimbo, M., Okado, M.: Crystal Base andq-Vertex Operators. Commun. Math. Phys.155, 47–69 (1993)

    Google Scholar 

  17. Chari, V., Pressley, A.: Quantum Affine Algebras. Commun. Math. Phys.142, 261–283 (1991)

    Google Scholar 

  18. Friedan, D., Martinec, E., Shenker, S.: Conformal Invariance, Supersymmetry and String Theory. Nucl. Phys.B271, 93–165 (1986)

    Google Scholar 

  19. Bernard, D., Felder, G.: Fock Representations and BRST Cohomology inSL(2) Current Algebra. Commun. Math. Phys.127, 145–168 (1990)

    Google Scholar 

  20. Matsuo, A.: Jackson Integrals of Jordan-Pochhammer Type and Knizhnik-Zamolodchikov Equations. Preprint (1992)

  21. Matsuo, A.: Quantum Algebra Structure of Certain Jackson Integrals. Preprint (1992)

  22. Reshetikhin, N.: Jackson-Type Integrals, Bethe Vectors, and Solutions to a Difference Analog of the Knizhnik-Zamolodchikov System. Preprint

  23. Mimachi, K.: Connection Problem in Holonomicq-Difference System Associated with a Jackson Integral of Jordan-Pochhammer Type. Nagoya Math. J.116, 149–161 (1989)

    Google Scholar 

  24. Tsuchiya, A., Kanie, Y.: Vertex Operators in Conformal Field Theory onP 1 and Monodromy Representations of Braid Group. Adv. Stud. Pure Math.16, 297–372 (1988)

    Google Scholar 

  25. Matsuo, A.: Free Field Realization of Quantum Affine Algebra Uq(sl2). Preprint (1992)

  26. Abada, A., Bougourzi, A.H., El Gradechi, M.A.: Deformation of the Wakimoto construction. Preprint (1992)

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Tokyo, Meguro-ku, 153, Tokyo, Japan

    Akishi Kato

  2. Department of Physics, University of Tokyo, Bunkyo-ku, 113, Tokyo, Japan

    Yas-Hiro Quano & Jun'ichi Shiraishi

Authors
  1. Akishi Kato
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  2. Yas-Hiro Quano
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  3. Jun'ichi Shiraishi
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Communicated by H. Araki

Partly supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 04245206)

A Fellow of the Japan Society of the Promotion of Science for Japanese Junior Scientists. Partly supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture (No. 04-2297)

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Kato, A., Quano, YH. & Shiraishi, J. Free boson representation ofq-vertex operators and their correlation functions. Commun.Math. Phys. 157, 119–137 (1993). https://doi.org/10.1007/BF02098022

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  • DOI: https://doi.org/10.1007/BF02098022

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