Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 5 (2009), 027, 21 pages      arXiv:0810.4748      https://doi.org/10.3842/SIGMA.2009.027

q-Wakimoto Modules and Integral Formulae of Solutions of the Quantum Knizhnik-Zamolodchikov Equations

Kazunori Kuroki
Department of Mathematics, Kyushu University, Hakozaki 6-10-1, Fukuoka 812-8581, Japan

Received October 31, 2008, in final form February 25, 2009; Published online March 07, 2009

Abstract
Matrix elements of intertwining operators between q-Wakimoto modules associated to the tensor product of representations of Uq(^sl2) with arbitrary spins are studied. It is shown that they coincide with the Tarasov-Varchenko's formulae of the solutions of the qKZ equations. The result generalizes that of the previous paper [Kuroki K., Nakayashiki A., SIGMA 4 (2008), 049, 13 pages].

Key words: free field; vertex operator; qKZ equation; q-Wakimoto module.

pdf (307 kb)   ps (231 kb)   tex (18 kb)

References

  1. Abada A., Bougourzi A.H., El Gradechi M.A., Deformation of the Wakimoto construction, Modern Phys. Lett. A 8 (1993), 715-724, hep-th/9209009.
  2. Bougourzi A.H., Weston R.A., Matrix elements of Uq(su(2)k) vertex operators via bosonization, Internat. J. Modern Phys. A 9 (1994), 4431-4447, hep-th/9305127.
  3. Frenkel I.B., Reshetikhin N.Yu., Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), 1-60.
  4. Idzumi M., Tokihiro T., Iohara K., Jimbo M., Miwa T., Nakashima T., Quantum affine symmetry in vertex models, Internat. J. Modern Phys. A 8 (1993), 1479-1511, hep-th/9208066.
  5. Jimbo M., Miwa T., Algebraic analysis of solvable lattice models, CBMS Regional Conference Series in Mathematics, Vol. 85, American Math. Soc., Providence, RI, 1995.
  6. Kato A., Quano Y.-H., Shiraishi J., Free boson representation of q-vertex operators and their correlation functions, Comm. Math. Phys. 157 (1993), 119-137, hep-th/9209015.
  7. Konno H., Free-field representation of the quantum affine algebra Uq(^sl2) and form factors in the higher-spin XXZ model, Nuclear Phys. B 432 (1994), 457-486, hep-th/9407122.
  8. Kuroki K., Nakayashiki A., Free field approach to solutions of the quantum Knizhnik-Zamolodchikov equations, SIGMA 4 (2008), 049, 13 pages, arXiv:0802.1776.
  9. Matsuo A., Quantum algebra structure of certain Jackson integrals, Comm. Math. Phys. 157 (1993), 479-498.
  10. Matsuo A., A q-deformation of Wakimoto modules, primary fields and screening operators, Comm. Math. Phys. 160 (1994), 33-48, hep-th/9212040.
  11. Shiraishi J., Free boson representation of quantum affine algebra, Phys. Lett. A 171 (1992), 243-248.
  12. Shiraishi J., Free boson realization of quantum affine algebras, PhD thesis, University of Tokyo, 1995.
  13. Tarasov V., Varchenko A., Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups, Astérisque 246 (1997), 1-135.

Previous article   Next article   Contents of Volume 5 (2009)