Holonomic $q$-difference system of the first order associated with a Jackson integral of Selberg type
Katsuhisa Mimachi
Source: Duke Math. J. Volume 73, Number 2
(1994), 453-468.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288818
Mathematical Reviews number (MathSciNet): MR1262214
Zentralblatt MATH identifier: 0801.39003
Digital Object Identifier: doi:10.1215/S0012-7094-94-07319-5
References
[1] K. Aomoto, Gauss-Manin connection of integral of difference products, J. Math. Soc. Japan 39 (1987), no. 2, 191–208.
Mathematical Reviews (MathSciNet): MR88f:32031
Zentralblatt MATH: 0619.32010
Digital Object Identifier: doi:10.2969/jmsj/03920191
Project Euclid: euclid.jmsj/1230130437
[2] K. Aomoto, A note on holonomic $q$-difference systems, Algebraic analysis, Vol. I, Academic Press, Boston, MA, 1988, pp. 25–28.
Mathematical Reviews (MathSciNet): MR90d:58145
Zentralblatt MATH: 0674.33006
[3] K. Aomoto, Finiteness of a cohomology associated with certain Jackson integrals, Tôhoku Math. J. (2) 43 (1991), no. 1, 75–101.
Mathematical Reviews (MathSciNet): MR92c:33035
Zentralblatt MATH: 0769.33016
Digital Object Identifier: doi:10.2748/tmj/1178227537
Project Euclid: euclid.tmj/1178227537
[4] K. Aomoto, $2$ conjectural formulae for symmetric $A$-type Jackson integrals, preprint.
[5] K. Aomoto, Y. Kato, and K. Mimachi, A solution of the Yang-Baxter equation as connection coefficients of a holonomic $q$-difference system, Internat. Math. Res. Notices (1992), no. 1, 7–15.
Mathematical Reviews (MathSciNet): MR93d:39007
Zentralblatt MATH: 0765.39002
Digital Object Identifier: doi:10.1155/S1073792892000023
[6] G. D. Birkhoff, The generalized Riemann problem for linear differential and the allied problems for linear difference and $q$- difference equations, Proc. Amer. Acad. Arts Sci. 49 (1914), 521–568.
Zentralblatt MATH: 44.0391.03
[7] R. D. Carmichael, The general theory of linear $q$-difference equations, Amer. J. Math. 34 (1912), 147–168.
Zentralblatt MATH: 43.0411.02
[8] E. Date, M. Jimbo, A. Matsuo, and T. Miwa, Hypergeometric type integrals and the $sl(2,\mathbbC)$ Knizhnik-Zamolodchikov equation, Internat. J. Modern Phys. B 4 (1990), no. 5, 1049–1057, Proceedings of the conference on Yang-Baxter equations, conformal invariance and integrability in statistical mechanics and field theory, World Scientific.
Mathematical Reviews (MathSciNet): MR92f:32063
Zentralblatt MATH: 0722.33007
Digital Object Identifier: doi:10.1142/S0217979290000528
[9] V. S. Dotsenko and V. A. Fateev, Conformal algebra and multipoint correlation functions in $2$D statistical models, Nuclear Phys. B 240 (1984), no. 3, 312–348.
Mathematical Reviews (MathSciNet): MR85i:82061
Digital Object Identifier: doi:10.1016/0550-3213(84)90269-4
[10] I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1–60.
Mathematical Reviews (MathSciNet): MR94c:17024
Zentralblatt MATH: 0760.17006
Digital Object Identifier: doi:10.1007/BF02099206
Project Euclid: euclid.cmp/1104249974
[11] G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia Math. Appl., vol. 35, Cambridge Univ. Press, Cambridge, 1990.
Mathematical Reviews (MathSciNet): MR91d:33034
Zentralblatt MATH: 0695.33001
[12] K. Kadell, A proof of Askey's conjectured $q$-analogue of Selberg's integral and a conjecture of Morris, SIAM J. Math. Anal. 19 (1988), no. 4, 969–986.
Mathematical Reviews (MathSciNet): MR89h:33006b
Zentralblatt MATH: 0643.33004
Digital Object Identifier: doi:10.1137/0519067
[13] J. Kaneko, Selberg integrals and hypergeometric functions, Special Differential Equations, Proceedings of the Taniguchi workshop, Kyushu Univ., 1992, pp. 62–68.
[14] A. Matsuo, Quantum algebra structure of certain Jackson integrals, preprint.
Mathematical Reviews (MathSciNet): MR1243708
Zentralblatt MATH: 0795.17023
Digital Object Identifier: doi:10.1007/BF02096880
Project Euclid: euclid.cmp/1104254019
[15] K. Mimachi, Connection problem in holonomic $q$-difference system associated with a Jackson integral of Jordan-Pochhammer type, Nagoya Math. J. 116 (1989), 149–161.
Mathematical Reviews (MathSciNet): MR91b:33023
Zentralblatt MATH: 0688.39002
Project Euclid: euclid.nmj/1118781433
[16] K. Mimachi, Holonomic $q$-difference system associated with the basic hypergeometric series $_ n+1\phi_ n$, to appear in Tôhoku Math. J. (2) 45.
Mathematical Reviews (MathSciNet): MR1245715
Digital Object Identifier: doi:10.2748/tmj/1178225842
Project Euclid: euclid.tmj/1178225842
[17] K. Mimachi, The little $q$-Jacobi polynomial associated with a $q$-Selberg integral, preprint.
Mathematical Reviews (MathSciNet): MR1627353
Zentralblatt MATH: 1142.33315
[18] T. Terasoma, Determinants of $q$-hypergeometric functions and another proof of Askey's conjecture, preprint.
Mathematical Reviews (MathSciNet): MR1483545
Zentralblatt MATH: 0892.33009
Digital Object Identifier: doi:10.1007/PL00004353
[19] W. J. Trjitzinsky, Analytic theory of linear $q$-difference equations, Acta Math. 61 (1933), 1–38.
Zentralblatt MATH: 0007.21103
[20] A. Varchenko, Multidimensional hypergeometric functions in conformal field theory, algebraic $K$-theory, algebraic geometry, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, pp. 281–300.
Mathematical Reviews (MathSciNet): MR93d:32060
Zentralblatt MATH: 0747.33002
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