Structure and duality of D-modules related to KP hierarchy

Toshikazu MIYAJIMA; Atsushi NAKAYASHIKI; Kanehisa TAKASAKI

doi:10.2969/jmsj/04340751

Toshikazu MIYAJIMA, Atsushi NAKAYASHIKI, Kanehisa TAKASAKI

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 4 Pages 751-773

DOI https://doi.org/10.2969/jmsj/04340751

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Published: 1991 Received: March 19, 1990 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: CITATION Details: Wrong : 1) E. Date, M. Kashiwara, M. Jimbo and T. Miwa, Transformation groups for soliton equations, in Nonlinear Integrable Systems-Classical Theory and Quantum Theory, Kyoto 1981, M. Jimbo and T. Miwa eds., World Scientific, Singapore, 1983.
2) M. Kashiwara, Algebraic study of systems of partial differential equations, Master's thesis, Tokyo University, 1971 (in Japanese).
3) M. Kashiwara, The flag manifold of Kac-Moody Lie algebras, Amer. J. Math., 111 (1989), (to appear).
4) E. R. Kolchin, Differential algebraic groups, Academic Press, New York, 1985.
5) T. Miyajima, Structure of P-modules related to Grassmannian manifolds, Master's thesis, Nagoya University, 1989 (in Japanese).
6) M. Mulase, Complete integrability of the Kadomtsev-Petviashvili equation, Adv, in Math., 54 (1984), 57-66.
7) Y. Ohyama. Self-duality and Integrable systems, Kyoto University preprint RIMS-678 (January, 1990).
8) M. Sato and Y. Sato, Soliton equations as dynamical systems in an infinite dimensional Grassmann manifold, in Nonlinear Partial Differential Equations in Applied Sciences, U. S.-Japan seminor, Tokyo 1982, P. D. Lax, H. Fujita, and G. Strang eds., North-Holland, Amsterdam and Kinokuniya, Tokyo, 1982.
9) M. Sato and M. Noumi, Soliton equations and universal Grassmann manifold, Sophia University Lecture Notes No. 18, Department of Mathematics, Sophia University, Tokyo, 1984 (in Japanese).
10) M. Sato, Lectures at Kyoto University 1984-85, Suri-Kaiseki Lecture Notes No. 5, Suri-Kaiseki Lecture Note Kankokai, 1989 (in Japanese).
11) M. Sato, The KP hierarchy and infinite dimensional Grassmann manifolds, Proc. Sympos. Pure Math., 49, American Mathematical Society, 1989.
12) M. Sato, P-modules and nonlinear systems, in Integrable systems in quantum theory and statistical mechanics, M. Jimbo, T. Miwa and A. Tsuchiya eds., Adv. Stud. Pure Math., 19, Kinokuniya, Tokyo, 1989.
13) G. Segal and G. Wilson, Loop groups and equations of KdV type, Publ, IHES, 61 (1985), 5-65.
14) K. Takasaki, Integrable systems as deformations of P-modules, Proc. Symp. Pure Math., 49, American Mathematical Society, 1989.

Right : [1] E. Date, M. Kashiwara, M. Jimbo and T. Miwa, Transformation groups for soliton equations, in Nonlinear Integrable Systems-Classical Theory and Quantum Theory, Kyoto 1981, M. Jimbo and T. Miwa eds., World Scientific, Singapore, 1983.
[2] M. Kashiwara, Algebraic study of systems of partial differential equations, Master's thesis, Tokyo University, 1971 (in Japanese).
[3] M. Kashiwara, The flag manifold of Kac-Moody Lie algebras, Amer. J. Math., 111 (1989), (to appear).
[4] E. R. Kolchin, Differential algebraic groups, Academic Press, New York, 1985.
[5] T. Miyajima, Structure of D-modules related to Grassmannian manifolds, Master's thesis, Nagoya University, 1989 (in Japanese).
[6] M. Mulase, Complete integrability of the Kadomtsev-Petviashvili equation, Adv, in Math., 54 (1984), 57-66.
[7] Y. Ohyama. Self-duality and integrable systems, Kyoto University preprint RIMS-678 (January, 1990).
[8] M. Sato and Y. Sato, Soliton equations as dynamical systems in an infinite dimensional Grassmann manifold, in Nonlinear Partial Differential Equations in Applied Sciences, U. S. -Japan seminor, Tokyo 1982, P. D. Lax, H. Fujita, and G. Strang eds., North-Holland, Amsterdam and Kinokuniya, Tokyo, 1982.
[9] M. Sato and M. Noumi, Soliton equations and universal Grassmann manifold, Sophia University Lecture Notes No. 18, Department of Mathematics, Sophia University, Tokyo, 1984 (in Japanese).
[10] M. Sato, Lectures at Kyoto University 1984-85, Suri-Kaiseki Lecture Notes No. 5, Suri-Kaiseki Lecture Note Kankokai, 1989 (in Japanese).
[11] M. Sato, The KP hierarchy and infinite dimensional Grassmann manifolds, Proc. Sympos. Pure Math., 49, American Mathematical Society, 1989.
[12] M. Sato, D-modules and nonlinear systems, in Integrable systems in quantum theory and statistical mechanics, M. Jimbo, T. Miwa and A. Tsuchiya eds., Adv. Stud. Pure Math., 19, Kinokuniya, Tokyo, 1989.
[13] G. Segal and G. Wilson, Loop groups and equations of KdV type, Publ, IHES, 61 (1985), 5-65.
[14] K. Takasaki, Integrable systems as deformations of D-modules, Proc. Symp. Pure Math., 49, American Mathematical Society, 1989.

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