On solutions of the KZ and qKZ equations at level zero
Nakayashiki, A. ; Pakuliak, S. ; Tarasov, V.
Annales de l'I.H.P. Physique théorique, Tome 71 (1999), p. 459-496 / Harvested from Numdam
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@article{AIHPA_1999__71_4_459_0,
     author = {Nakayashiki, A. and Pakuliak, S. and Tarasov, V.},
     title = {On solutions of the KZ and qKZ equations at level zero},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {71},
     year = {1999},
     pages = {459-496},
     mrnumber = {1721551},
     zbl = {0941.35089},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1999__71_4_459_0}
}

Nakayashiki, A.; Pakuliak, S.; Tarasov, V. On solutions of the KZ and qKZ equations at level zero. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) pp. 459-496. http://gdmltest.u-ga.fr/item/AIHPA_1999__71_4_459_0/

[1] A. Chervov, Traces of creating-annihilating operators and Fredholm's formulas, Preprint (1997) 1-20, q-alg/9703017.

[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. | MR 1201657 | Zbl 0769.17020

[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. B 4 (1990) 1049-1057. | MR 1064760 | Zbl 0722.33007

[4] I. Frenkel and N. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992) 1-60. | MR 1163666 | Zbl 0760.17006

[5] K. Iohara and M. Kohno, A central extension of Yangian double and its vertex representations, Lett. Math. Phys. 37 (1996) 319-328. | MR 1392590 | Zbl 0867.17013

[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. A 27 (1994) 3267- 3283. | MR 1282167 | Zbl 0842.17030

[7] M. Jimbo and T. Miwa, Algebraic analisys of solvable lattice models, Conference Board of the Mathem. Sciences, Regional Conference Series in Mathematics 85 ( 1995). | MR 1308712 | Zbl 0828.17018

[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. A 29 (1996) 2923- 2958. | MR 1398600 | Zbl 0896.35114

[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. | MR 1384643 | Zbl 0887.17007

[10] S. Khoroshkin, D. Lebedev and S. Pakuliak, Traces of intertwining operators for the Yangian double, Lett. Math. Phys. 41 (1997) 31-47. | MR 1455030 | Zbl 0973.17022

[11] T. Kojima and Y.-H. Quano, Quantum Knizhnik-Zamolodchikov equation for Uq(sln) and integral formula, J. Phys. A 27 (1994) 6807-6826. | MR 1306832 | Zbl 0844.17011

[12] S. Lukyanov, Free field representation for massive integrable models, Comm. Math. Phys. 167 (1995) 183-226. | MR 1316504 | Zbl 0818.46079

[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. | MR 1422360 | Zbl 0889.17009

[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] 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. | MR 1658129 | Zbl 0959.32028

[16] A. Nakayashiki, Some integral formulas for the solutions of the sl2 dKZ equation with level -4, Int. J. Mod. Phys. A 9 (1994) 5673-5687. | MR 1306785 | Zbl 0985.82504

[17] F.A. Smirnov, Form Factors in Completely Integrable Field Theories, World Scientific, Singapore, 1992. | MR 1253319

[18] F. Smirnov, Counting the local fields in SG theory, Nucl. Phys. B 453 (1995) 807- 824. | MR 1358784 | Zbl 1003.81545

[19] F. Smirnov, Dynamical symmetries of massive integrable models. I, Adv. Ser. Math. Phys. 16 (1992) 813-837. | MR 1187577

[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. | MR 1145242

[21] V. Schechtman and A. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991) 139-194. | MR 1123378 | Zbl 0754.17024

[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. | MR 1290820 | Zbl 0824.33012

[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. | MR 1452432 | Zbl 0877.33013

[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. | MR 1646561

[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. | MR 1277474 | Zbl 0807.17014