| Project/Area Number |
11304007
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kobe University |
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Principal Investigator |
NOUMI Masatoshi Kobe University, Graduate School of Science and Technology, Professor, 大学院・自然科学研究科, 教授 (80164672)
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Masahiko Faculty of Science, Professor, 理学部, 教授 (80183044)
SASAKI Takeshi Faculty of Science, Professor, 理学部, 教授 (00022682)
TAKANO Kyoichi Faculty of Science, Professor, 理学部, 教授 (10011678)
MASUDA Tetsu Graduate School of Science and Technology, Assistant, 大学院・自然科学研究科, 助手 (00335457)
YAMADA Yasuhiko Faculty of Science, Professor, 理学部, 教授 (00202383)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Painleve equation / affine Weyl group symmetry / hypergeometric equation / configuration space / integrable system |
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| Research Abstract |
Main achievements of this research are summarized as follows.
1. Affine Weyl group symmetry of Painleve systems: Generalizing the structure of Backlund transformations for Painleve equations, Noumi and Yamada proposed a universal framework of Weyl group symmetry as groups of birational transformations. This class of groups of birational transformations is defined in terms of root systems, and has its origin in Kac-Moody groups. Also, they found a method for constructing a class of nonlinear (partial) differential equations of Painleve type by similarity reduction from the infinite integrable systems of Drinfeld-Sokolov. This work brought out a new unified point of view on the Lie theoretic background of the symmetry of Painleve equations.
2. Geometric aspects of hypergeometric and Painleve systems: In the joint work with Yoshida, Sasaki constructed the uniformizing differential equation for the moduli space of cubic surfaces. This system of linear differential equations, with Weyl group symmetry of type E_6, arises as a subsystem of the hypergeometric system of type E(3, 6) associated with hyperplane configurations. On the basis of Sakai's geometric approach to Painleve equations, Saito and others found a method of constructing the Painleve equations and their defining manifolds from the algebraic- geometric theory of deformations of rational surfaces.
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