On solutions of the KZ and qKZ equations at level zero

A. Nakayashiki; S. Pakuliak; V. Tarasov

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 4, page 459-496
  • ISSN: 0246-0211

How to cite

top

Nakayashiki, A., Pakuliak, S., and Tarasov, V.. "On solutions of the KZ and qKZ equations at level zero." Annales de l'I.H.P. Physique théorique 71.4 (1999): 459-496. <http://eudml.org/doc/76842>.

@article{Nakayashiki1999,
author = {Nakayashiki, A., Pakuliak, S., Tarasov, V.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {quantum Knizhnik-Zamolodchikov difference equations at level zero; rational solutions of the Yang-Baxter equations; integral formulae for solutions of the qKZ equations},
language = {eng},
number = {4},
pages = {459-496},
publisher = {Gauthier-Villars},
title = {On solutions of the KZ and qKZ equations at level zero},
url = {http://eudml.org/doc/76842},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Nakayashiki, A.
AU - Pakuliak, S.
AU - Tarasov, V.
TI - On solutions of the KZ and qKZ equations at level zero
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 4
SP - 459
EP - 496
LA - eng
KW - quantum Knizhnik-Zamolodchikov difference equations at level zero; rational solutions of the Yang-Baxter equations; integral formulae for solutions of the qKZ equations
UR - http://eudml.org/doc/76842
ER -

References

top
  1. [1] A. Chervov, Traces of creating-annihilating operators and Fredholm's formulas, Preprint (1997) 1-20, q-alg/9703017. 
  2. [2] B. Davies, O. Foda, M. Jimbo, T. Miwa and A. Nakayashiki, Diagonalization of the XXZ Hamiltonian by vertex operators, Comm. Math. Phys.151 (1993) 89-153. Zbl0769.17020MR1201657
  3. [3] E. Date, M. Jimbo, A. Matsuo and T. Miwa, Hypergeometric type integrals and the sl(2, C) Knizhnik-Zamolodchikov equations, Int. J. Mod. Phys. B4 (1990) 1049-1057. Zbl0722.33007MR1064760
  4. [4] I. Frenkel and N. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys.146 (1992) 1-60. Zbl0760.17006MR1163666
  5. [5] K. Iohara and M. Kohno, A central extension of Yangian double and its vertex representations, Lett. Math. Phys.37 (1996) 319-328. Zbl0867.17013MR1392590
  6. [6] M. Jimbo, T. Kojima, T. Miwa and Y.-H. Quano, Smirnov's integrals and the quantum Knizhnik-Zamolodchikov equation of level 0, J. Phys. A27 (1994) 3267- 3283. Zbl0842.17030MR1282167
  7. [7] M. Jimbo and T. Miwa, Algebraic analisys of solvable lattice models, Conference Board of the Mathem. Sciences, Regional Conference Series in Mathematics85 ( 1995). Zbl0828.17018MR1308712
  8. [8] M. Jimbo and T. Miwa, Quantum KZ equation with |q| = 1 and correlation functions of the XXZ model in the gapless regime, J. Phys. A29 (1996) 2923- 2958. Zbl0896.35114MR1398600
  9. [9] S. Khoroshkin, Central extension of the Yangian double, in: Collection SMF, Colloque "Septièmes Rencontres du Contact Franco-Belge en Algèbre", June 1995, Reins; Preprint (1996) 1-12, q-alg/9602031. Zbl0887.17007MR1384643
  10. [10] S. Khoroshkin, D. Lebedev and S. Pakuliak, Traces of intertwining operators for the Yangian double, Lett. Math. Phys.41 (1997) 31-47. Zbl0973.17022MR1455030
  11. [11] T. Kojima and Y.-H. Quano, Quantum Knizhnik-Zamolodchikov equation for Uq(sln) and integral formula, J. Phys. A27 (1994) 6807-6826. Zbl0844.17011MR1306832
  12. [12] S. Lukyanov, Free field representation for massive integrable models, Comm. Math. Phys.167 (1995) 183-226. Zbl0818.46079MR1316504
  13. [13] K. Mimachi, A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type, Duke Math. J.85 (1996) 635-658. Zbl0889.17009MR1422360
  14. [14] E. Mukhin and A. Varchenko, On algebraic equations satisfied by hypergeometric solutions of the qKZ equation, Preprint (1997) 1-20, q-alg/9710040; Quantization of the space of conformal blocks Preprint (1997) 1-9, q-alg/9710039; The quantized Knizhnik-Zamolodchikov equation in tensor products of irreducible sl(2)-modules Preprint (1997) 1-32, q-alg/9709026. 
  15. [15] A. Nakayashiki, Integral and theta formulae for solutions of slN Knizhnik-Zamolodchikov equation at level zero, Publ. Res. Inst. Math. Sci.34 (1998) 439- 486. Zbl0959.32028MR1658129
  16. [16] A. Nakayashiki, Some integral formulas for the solutions of the sl2 dKZ equation with level -4, Int. J. Mod. Phys. A9 (1994) 5673-5687. Zbl0985.82504MR1306785
  17. [17] F.A. Smirnov, Form Factors in Completely Integrable Field Theories, World Scientific, Singapore, 1992. Zbl0788.46077MR1253319
  18. [18] F. Smirnov, Counting the local fields in SG theory, Nucl. Phys. B453 (1995) 807- 824. Zbl1003.81545MR1358784
  19. [19] F. Smirnov, Dynamical symmetries of massive integrable models. I, Adv. Ser. Math. Phys.16 (1992) 813-837. Zbl0925.17027MR1187577
  20. [20] F. Smirnov, Lectures on integrable massive models of quantum field theory, in: M.-L. Ge and B.-H. Zhao, eds., Nankai Lectures on Mathem. Physics, World Scentific, Singapore, 1990, pp. 1-68. MR1145242
  21. [21] V. Schechtman and A. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math.106 (1991) 139-194. Zbl0754.17024MR1123378
  22. [22] V. Tarasov and A. Varchenko, Jackson integral representations of solutions of the quantized Knizhnik-Zamolodchikov equation, St. Petersburg Math. J.6 (1995) 275-313. Zbl0824.33012MR1290820
  23. [23] V. Tarasov and A. Varchenko, Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math.128 (1997) 501-588. Zbl0877.33013MR1452432
  24. [24] V. Tarasov and A. Varchenko, Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups, Preprint (1997) 1-69; to appear in Asterisque, q-alg/9703044. Zbl0938.17012MR1646561
  25. [25] A. Varchenko, Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for q-hypergeometric functions, Comm. Math. Phys.162 (1994) 499-528. Zbl0807.17014MR1277474

NotesEmbed ?

top

You must be logged in to post comments.