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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)
K. Aomoto, Y. Kato: Gauss decomposition of connection matrices for symmetric A-type Jackson integrals. Preprint 1–45 (1995)
V. Chari, A. Pressley: A guide to quantum groups. Cambrige University Press, Cambridge, 1994
V.G. Drinfeld: Quantum groups. In: Proceedings of ICM, Berkley, 1986 (A.M. Gleason, ed.), AMS, Providence, 798–820 (1987)
V.G. Drinfeld: Quasi-Hopf algebras. Leningrad Math. J. 1 1419–1457 (1990)
J. Ding, LB. Frenkel: Isomorphism of two realizations of quantum affine algebra , Comm. Math. Phys. 156, 277–300
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)
I.B. Frenkel, N.Yu. Reshetikhin: Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146, 1–60 (1992)
L.D. Faddeev, L.A. Takhtajan, V.O. Tarasov: Local Hamiltonians for integrable models on a lattice, Theor. Math. Phys. 57, 1059–1072 (1983)
G. Felder, V. Tarasov, A. Varchenko: Bethe ansatz for interaction-round-a-face elliptic models and solutions to qKZB equations. In preparation
G. Felder, A. Varchenko: On representations of the elliptic quantum group E τ,ν(sl 2). Preprint 1–21 (1995)
R.A. Gustafson: A generalization of Selbergs’s beta integral, Bull. Amer. Math. Society 22, 97–105 (1990)
G. Gasper, M. Rahman: Basic hypergeometric series, Encycl, Math. Appl., Cambrige University Press, Cambridge, 1990
M. Jimbo, T. Miwa: Algebraic analysis of solvable lattice models, CBMS Regional Conf. Series in Math. 85 (1995)
A. Izergin, V.E. Korepin: The quantum scattering method approach to correlation functions, Comm. Math. Phys. 94, 67–92 (1984)
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)
K. Kadell: A proof of Askey’s conjectured q-analogue of Selberg’s integral and a conjecture of Morris, SLAM J. Math. Anal. 19, 969–986 (1988)
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)
V.E. Korepin: Calculations of norms of Bethe wave functions, Comm. Math. Phys. 86, 391–418 (1982)
P.P. Kulish, N.Yu. Reshetikhin, E.K. Sklyanin: Yang-Baxter equation and representation theory I, Lett. Math. Phys. 5, 393–403 (1981)
D. Kazhdan, Ya.S. Soibelman: Representations of the quantized function algebras. 2-categories and Zamolodchikov tetrahedra equation. Preprint, Harvard University 1–66 (1992)
F. Loeser: Arrangements d’hyperplans et sommes de Gauss, Ann. Scient. École Normale Super. 4-e serie, t. 24, 379–400 (1991)
S. Lukyanov: Free field representation for massive integrable models, Comm. Math. Phys. 167, 183–226 (1995)
A. Matsuo: Jackson integrals of Jordan-Pockhgammer type and quantum Knizhnik-Zamolodchikov equation, Comm. Math. Phys. 151, 263–274 (1993)
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)
N.Yu. Reshetikhin, L.D. Faddeev: Hamiltonian structures for integrable field theory models, Theor. Math. Phys. 56, 847–862 (1983)
N.Yu. Reshetikhin, M.A. Semenov-Tyan-Shansky: Central extensions of the quantum current groups, Lett. Math. Phys. 19, 133–142 (1990)
F.A. Smirnov: Form factors in completely integrable models of quantum field theory, Advanced Series in Math. Phys., vol. 14, World Scientific, Singapore, 1992
A. Selberg: Bemerkninger om et multipelt integral, Norsk. Mat. Tidsskr. 26, 71–78 (1944)
V.V. Schechtman, A.N. Varchenko: Hypergeometric solutions of Knizhnik-Zamolodchikov equations, Lett. Math. Phys. 20, 279–283 (1990)
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
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)
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)
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)
V. Tarasov, A. Varchenko: Geometry of q-hypergeometric functions as a bridge between quantum affine algebras and elliptic quantum affine algebras. In preparation
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)
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
A. Varchenko: Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for p-hypergeometric functions, Comm. Math. Phys. 162, 499–528 (1994)
A. Varchenko: Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base, Comm. Math. Phys. 171, 99–137 (1995)
E.T. Whittaker, G.N. Watson: A Course of Modern Analysis. Cambrige University Press, Cambribge, 1927
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Oblatum 20-V-1996 ⇐p; 7-VIII-1996
On leave of absence from St. Petersburg Branch of Steklov Mathematical Institute, supported in part by MAE-MICECO-CNRS Fellowship
Supported in part by NSF grant DMS-9501290
URA 14-36 du CNRS associée à l’E.N.S. de Lyon, au LAPP d’Annecy et à l’Universitè de Savoie
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Tarasov, V., Varchenko, A. Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras. Invent. math. 128, 501–588 (1997). https://doi.org/10.1007/s002220050151
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DOI: https://doi.org/10.1007/s002220050151