Gauss-Manin connection of integral of difference products

Kazuhiko AOMOTO

doi:10.2969/jmsj/03920191

Kazuhiko AOMOTO

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JOURNAL FREE ACCESS

1987 Volume 39 Issue 2 Pages 191-208

DOI https://doi.org/10.2969/jmsj/03920191

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Published: 1987 Received: August 14, 1985 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Nagayoshi Iwahori on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [A1] K. Aomoto, Un théorème du type de M-M concernant l'intégrale des fonctions multiformes, J. Math. Pures Appl., 52 (1973), 1-11.
[A2] K. Aomoto, On the vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
[A3] K. Aomoto, Les équations aux différences linéaires et les integrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, 26 (1975), 271-297.
[A4] K. Aomoto, On the structure of integrals of power product of linear functions, Sci. Papers College Gen. Ed. Univ. Tokyo, 27 (1977), 49-61.
[A5] K. Aomoto, Configurations and invariant theory of Gauss-Manin systems, Group pepresentations and systems of differential equations, Adv. Studies in Pure Math., 4, 1984, pp. 169-179.
[A6] R. S. Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math., 11 (1980), 938-951.
[D] P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy, preprint, I. H. E. S., 1983.
[J] M. Jimbo, T. Miwa, Y. Mori and M. Sato, Density matrix of an impenetrable Bose-gas and the fifth Painlevé transcendent, Physica 1D, 1980, 80-158.
[K1] T. Kohno, Série de Poincaré-Koszul aux groupes de tresse pures, Invent. Math., 82 (1985), 57-75.
[K2] T. Kohno, Homology of a local system on the complement of hyperplanes, Proc. Japan Acad., 62 (1986), 145-147.
[O] Ka. Okamoto, On the polynomial Hamiltonian structure of the Gamier systems, J. Math. Pures Appl., 63 (1984), 129-146.
[S] A. Selberg, Bemerkniger om et multiplelt integral, Nordisk Mat. Tidskr., 26 (1944), 71-78.
[T] A. Tsuchiya and Y. Kanie, Fock space representation of the Virasoro algebra-Intertwining operators, Publ. Res. Inst. Math. Sci., 22 (1986), 259-327.

Right : [A1] K. Aomoto, Un théorème du type de M-M concernant l'intégrale des fonctions multiformes, J. Math. Pures Appl., 52 (1973), 1-11.
[A2] K. Aomoto, On the vanishing of cohomology attached to certain many valued meromorphic functions, J. Math. Soc. Japan, 27 (1975), 248-255.
[A3] K. Aomoto, Les équations aux différences linéaires et les integrales des fonctions multiformes, J. Fac. Sci. Univ. Tokyo, 26 (1975), 271-297.
[A4] K. Aomoto, On the structure of integrals of power product of linear functions, Sci. Papers College Gen. Ed. Univ. Tokyo, 27 (1977), 49-61.
[A5] K. Aomoto, Configurations and invariant theory of Gauss-Manin systems, Group pepresentations and systems of differential equations, Adv. Studies in Pure Math., 4, 1984, pp. 169-179.
[A6] R. S. Askey, Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math., 11 (1980), 938-951.
[D] P. Deligne and G. D. Mostow, Monodromy of hypergeometric functions and non-lattice integral monodromy, preprint, I. H. E. S., 1983.
[J] M. Jimbo, T. Miwa, Y. Mori and M. Sato, Density matrix of an impenetrable Bose-gas and the fifth Painlevé transcendent, Physica 1D, 1980, 80-158.
[K1] T. Kohno, Série de Poincaré-Koszul aux groupes de tresse pures, Invent. Math., 82 (1985), 57-75.
[K2] T. Kohno, Homology of a local system on the complement of hyperplanes, Proc. Japan Acad., 62 (1986), 145-147.
[O] Ka. Okamoto, On the polynomial Hamiltonian structure of the Garnier systems, J. Math. Pures Appl., 63 (1984), 129-146.
[S] A. Selberg, Bemerkniger om et multiplelt integral, Nordisk Mat. Tidskr., 26 (1944), 71-78.
[T] A. Tsuchiya and Y. Kanie, Fock space representation of the Virasoro algebra-Intertwining operators, Publ. Res. Inst. Math. Sci., 22 (1986), 259-327.

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