Rational singularities, Young diagram, Painleve equation

有理奇点、Young 图、Painleve 方程

• 批准号: 11440006
• 负责人: UMEMURA Hiroshi
• 金额: $ 9.28万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11440006/
• 关键词: Painleve equation; Young diagram; Special polynomial; Rational singular puint; Algebrait surface; パンルベ方程式; 微分ガロア理論; パーノルベ方程式

1. Painleve equations and Special polynomialWe 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 symmetriesNoumi 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 tranhformationsWe proved that the Backhund transformations arise from deformation of rational double points.4. Infinite dimensional differential Galois theory and Painleve equationsWe applied our theory of infinite dimensional to the definition of the Painleve equations.

1. 疼痛级方程和特殊多项式我们发现疼痛级方程生成特殊多项式。如果我们考虑发现Painleve方程的动机，它们具有组合方面是令人惊讶的。我们提出了一些关于特殊多项式的猜想并证明了它们。基于对称性的Painleve方程的推广，noumi认为这些猜想应该在一个自然框架中求解。为此，他从李代数理论的角度对Painleve方程进行了推广。有理双点的变形与Backhand变换证明了Backhand变换是由有理双点的变形引起的。无限维微分伽罗瓦理论与Painleve方程我们将无限维微分伽罗瓦理论应用于Painleve方程的定义。

项目成果

野海正俊 他: "Symmetries in the fourth Painleve equation and Okamoto polynomiouls"Nagoya Math. J.. 153. 53-86 (1999)

Masatoshi Noumi 等：“第四 Painleve 方程和冈本多项式中的对称性”Nagoya Math J.. 153. 53-86 (1999)

Hiroshi Umemura, Kazuo Okamoto, et al: "Special polynomials and Hirota bilinear relations of the second and the fourth Puinleve equations"Nagoya Math.J.. 159. 179-200 (2000)

Hiroshi Umemura、Kazuo Okamoto 等：“第二和第四 Puinleve 方程的特殊多项式和 Hirota 双线性关系”Nagoya Math.J. 159. 179-200 (2000)

Kazuo Okamoto et al.: "The puof of the Painleve propeit. Masuo Hukuhara"Funkcial.Ekuac. 44. 201-217 (2001)

Kazuo Okamoto 等人：“Painleve propeit 的 puof。Masuo Hukuhara”Funkcial.Ekuac。

Masatoshi Noumi et al.: "Symmetries in the fourth Painleve equations and Okamoto polynomials"Nagoya Math.J.. 153. 53-86 (1999)

Masatoshi Noumi 等：“第四 Painleve 方程和 Okamoto 多项式中的对称性”Nagoya Math.J.. 153. 53-86 (1999)

H.Umemura et al.: "Special polynomials nelated with the second and the Sourth Pounleve equationw"Nagoya Math.J.. 159. 179-200 (2000)

H.Umemura 等：“与第二次和南 Pounleve 方程相关的特殊多项式”Nagoya Math.J. 159. 179-200 (2000)