Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras

Inventiones Mathematicae

Volumn 128, Issue 3, 1997, Pages 501-588

  Tarasov, V ^a,b   Varchenko, A ^c  

^a UNIVERSITÉ DE LYON   (France)

^b UNIVERSITY OF NORTH CAROLINA   (United States)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031516992     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050151     Document Type: Article

References (48)

1. K. Aomoto: q-analogue of de Rham cohomology associated with Jackson Integrals, I, Proceedings of Japan Acad. 66 Ser. A (1990), 161-164; II, Proceedings of Japan Acad. 66 Ser. A, 240-244 (1990)
2. K. Aomoto: q-analogue of de Rham cohomology associated with Jackson Integrals, I, Proceedings of Japan Acad. 66 Ser. A (1990), 161-164; II, Proceedings of Japan Acad. 66 Ser. A, 240-244 (1990)
3. K. Aomoto, Y. Kato: Gauss decomposition of connection matrices for symmetric A-type Jackson integrals. Preprint 1-45 (1995)
4. V. Chari, A. Pressley: A guide to quantum groups. Cambrige University Press, Cambridge, 1994
5. V.G. Drinfeld: Quantum groups. In: Proceedings of ICM, Berkley, 1986 (A.M. Gleason, ed.), AMS, Providence, 798-820 (1987)
6. V.G. Drinfeld: Quasi-Hopf algebras. Leningrad Math. J. 1 1419-1457 (1990)
7. q(fraktur g signfraktur l sign(n)), Comm. Math. Phys. 156, 277-300
8. G. Felder: Elliptic quantum groups. Preprint hep-th/9412207 (1994); Proceedings of the ICMP, Paris, 1994 (to appear) G. Felder: Conformal field theory and integrable systems associated to elliptic curves. Preprint hep-th/9407154 (1994); Proceedings of the ICM, Zurich, 1994 (to appear)
9. G. Felder: Elliptic quantum groups. Preprint hep-th/9412207 (1994); Proceedings of the ICMP, Paris, 1994 (to appear) G. Felder: Conformal field theory and integrable systems associated to elliptic curves. Preprint hep-th/9407154 (1994); Proceedings of the ICM, Zurich, 1994 (to appear)
10. I.B. Frenkel, N.Yu. Reshetikhin: Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146, 1-60 (1992)
11. L.D. Faddeev, L.A. Takhtajan, V.O. Tarasov: Local Hamiltonians for integrable models on a lattice, Theor. Math. Phys. 57, 1059-1072 (1983)
12. G. Felder, V. Tarasov, A. Varchenko: Bethe ansatz for interaction-round-a-face elliptic models and solutions to qKZB equations. In preparation
13. τ,η(sl2). Preprint 1-21 (1995)
14. R.A. Gustafson: A generalization of Selbergs's beta integral, Bull. Amer. Math. Society 22, 97-105 (1990)
15. G. Gasper, M. Rahman: Basic hypergeometric series, Encycl, Math. Appl., Cambrige University Press, Cambridge. 1990
16. M. Jimbo, T. Miwa: Algebraic analysis of solvable lattice models, CBMS Regional Conf. Series in Math. 85 (1995)
17. A. Izergin, V.E. Korepin: The quantum scattering method approach to correlation functions, Comm. Math. Phys. 94, 67-92 (1984)
18. T. Kohno: Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier 37, 139-160 (1987) T. Kohno: Linear representations of braid groups and classical Yang-Baxter equations, Contemp. Math. 78, 339-363 (1988)
19. T. Kohno: Monodromy representations of braid groups and Yang-Baxter equations, Ann. Inst. Fourier 37, 139-160 (1987) T. Kohno: Linear representations of braid groups and classical Yang-Baxter equations, Contemp. Math. 78, 339-363 (1988)
20. K. Kadell: A proof of Askey's conjectured q-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Anal. 19, 969-986 (1988)
21. D. Kazhdan, G. Lusztig: Affine Lie algebras and quantum groups. Intern. Math. Research Notices 2, 21-29 (1991) D. Kazhdan, G. Lusztig: Tensor structures arising from affine Lie algebras, I. J. Amer. Math. Society 6 (1993), 905-947; II, J. Amer. Math. Society 6, 949-1011 (1993)
22. D. Kazhdan, G. Lusztig: Affine Lie algebras and quantum groups. Intern. Math. Research Notices 2, 21-29 (1991) D. Kazhdan, G. Lusztig: Tensor structures arising from affine Lie algebras, I. J. Amer. Math. Society 6 (1993), 905-947; II, J. Amer. Math. Society 6, 949-1011 (1993)
23. D. Kazhdan, G. Lusztig: Affine Lie algebras and quantum groups. Intern. Math. Research Notices 2, 21-29 (1991) D. Kazhdan, G. Lusztig: Tensor structures arising from affine Lie algebras, I. J. Amer. Math. Society 6 (1993), 905-947; II, J. Amer. Math. Society 6, 949-1011 (1993)
24. V.E. Korepin: Calculations of norms of Bethe wave functions, Comm. Math. Phys. 86, 391-418 (1982)
25. P.P. Kulish, N.Yu. Reshetikhin, E.K. Sklyanin: Yang-Baxter equation and representation theory I, Lett. Math. Phys. 5, 393-403 (1981)
26. D. Kazhdan, Ya.S. Soibelman: Representations of the quantized function algebras. 2-categories and Zamolodchikov tetrahedra equation. Preprint, Harvard University 1-66 (1992)
27. F. Loeser: Arrangements d'hyperplans et sommes de Gauss, Ann. Scient. École Normale Super. 4-e serie, t. 24, 379-400 (1991)
28. S. Lukyanov: Free field representation for massive integrable models, Comm. Math. Phys. 167, 183-226 (1995)
29. A. Matsuo: Jackson integrals of Jordan-Pockhgammer type and quantum Knizhnik-Zamolodchikov equation, Comm. Math. Phys. 151, 263-274 (1993)
30. N.Yu. Reshetikhin: Jackson-type integrals. Bethe vectors, and solutions to a difference analogue of the Knizhnik-Zamolodchikov system, Lett. Math. Phys. 26, 153-165 (1992)
31. N.Yu. Reshetikhin, L.D. Faddeev: Hamiltonian structures for integrable field theory models, Theor. Math. Phys. 56, 847-862 (1983)
32. N.Yu. Reshetikhin, M.A. Semenov-Tyan-Shansky: Central extensions of the quantum current groups, Lett. Math. Phys. 19, 133-142 (1990)
33. F.A. Smirnov: Form factors in completely integrable models of quantum field theory, Advanced Series in Math. Phys., vol. 14, World Scientific, Singapore, 1992
34. A. Selberg: Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 26, 71-78 (1944)
35. V.V. Schechtman, A.N. Varchenko: Hypergeometric solutions of Knizhnik-Zamolodchikov equations, Lett. Math. Phys. 20, 279-283 (1990)
36. V.V. Schechtman, A.N. Varchenko: Arrangements of hyperplanes and Lie algebras homology. Invent. Math. 106, 139-194 (1991) V.V. Schechtman, A.N. Varchenko: Quantum groups and homology of local systems. Algebraic Geometry and Analytic Geometry, ICM-90, Satellite Confer. Proceedings, Tokyo, 1990, Springer-Verlag, 182-191, 1991
37. V.V. Schechtman, A.N. Varchenko: Arrangements of hyperplanes and Lie algebras homology. Invent. Math. 106, 139-194 (1991) V.V. Schechtman, A.N. Varchenko: Quantum groups and homology of local systems. Algebraic Geometry and Analytic Geometry, ICM-90, Satellite Confer. Proceedings, Tokyo, 1990, Springer-Verlag, 182-191, 1991
38. V.O. Tarasov: Irreducible monodromy matrices for the R-matrix of the XXZ-model and lattice local quantum Hamiltonians, Theor. Math. Phys. 63, 440-454 (1985)
39. V.O. Tarasov, A.N. Varchenko: Jackson integral representations for solutions to the quantized Knizhnik-Zamolodchikov equation, St. Petersburg Math. J. 6, no. 2, 275-313 (1995)
40. V. Tarasov, A. Varchenko: Asymptotic solution to the quantized Knizhnik-Zamolodchikov equation and Bethe vectors. Preprint HU-TFT-94-21, UTMS 94-26 (1994); Advances in Soviet Math. (to appear)
41. V. Tarasov, A. Varchenko: Geometry of q-hypergeometric functions as a bridge between quantum affine algebras and elliptic quantum affine algebras. In preparation
42. A.N. Varchenko: The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes, I. Math. of the USSR, Izvestia 35, 543-571 (1990); II, Math. of the USSR Izvestia 36, 155-168 (1991) A.N. Varchenko: Determinant formula for Selberg type integrals, Funct. Anal. Appl. 4, 65-66 (1991)
43. A.N. Varchenko: The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes, I. Math. of the USSR, Izvestia 35, 543-571 (1990); II, Math. of the USSR Izvestia 36, 155-168 (1991) A.N. Varchenko: Determinant formula for Selberg type integrals, Funct. Anal. Appl. 4, 65-66 (1991)
44. A.N. Varchenko: The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes, I. Math. of the USSR, Izvestia 35, 543-571 (1990); II, Math. of the USSR Izvestia 36, 155-168 (1991) A.N. Varchenko: Determinant formula for Selberg type integrals, Funct. Anal. Appl. 4, 65-66 (1991)
45. A. Varchenko: Multidimensional hypergeometric functions and representation theory of Lie algebras and quantum groups, Advanced Series in Math. Phys., vol. 21, World Scientific, Singapore, 1995
46. A. Varchenko: Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for q-hypergeometric functions, Comm. Math. Phys. 162, 499-528 (1994)
47. A. Varchenko: Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base, Comm. Math. Phys. 171, 99-137 (1995)
48. E.T. Whittaker, G.N. Watson: A Course of Modern Analysis. Cambrige University Press, Cambribge, 1927