2002 Fiscal Year Final Research Report Summary
Rational singularities, Young diagram, Painleve equation
| Project/Area Number |
11440006
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
UMEMURA Hiroshi Nagoya University, Graduate school of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (40022678)
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| Co-Investigator(Kenkyū-buntansha) |
NOUMI Masatoshi Department of Mathematics, Kobe University, Professor, 理学部, 教授 (80164672)
OKAMOTO Kazuo Graduate school of Mathematical science, University of Tokyo Professor, 大学院・数理科学研究科, 教授 (40011720)
MUKAI Shigeru Research Institute of Mathematical Science, Kyoto University, Professor, 数理解析研究所, 教授 (80115641)
OKADA Soichi Nagoya University, Graduate school of Mathematics, Associated Professor, 大学院・多元数理科学研究科, 助教授 (20224016)
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| Project Period (FY) |
1999 – 2002
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| Keywords | Painleve equation / Young diagram / Special polynomial / Rational singular puint / Algebrait surface |
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| Research Abstract |
1. Painleve equations and Special polynomial
We disocvered that the Painleve equations generate special polynomials. If we consider the motivation of the discovery of the Painleve equtions, it is surprising that they have combinatorial aspects. We presented conjectures on the special polynomials and proved them.
2. Generalization of the Painleve equations based on the symmetries
Noumi considered that the conjectures should be solved in a natural frame work. To this end, he generalized the Painleve equations from the view point of theory of Lie algebra.
3. Deformation of rational double points and Backhand tranhformations
We proved that the Backhund transformations arise from deformation of rational double points.
4. Infinite dimensional differential Galois theory and Painleve equations
We applied our theory of infinite dimensional to the definition of the Painleve equations.
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