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.Painleve方程与特殊多项式我们发现Painleve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。提出了关于特殊多项式的猜想，并证明了猜想的正确性。基于对称的Painleve方程的推广Noumi认为猜想应该在自然的框架内求解。为此，他从李代数理论的角度推广了Painleve方程。有理双点的变形与反手变换我们证明了Backhund变换源于有理双点的变形。无限维微分伽罗瓦理论与Painleve方程我们将我们的无穷维理论应用于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。

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)

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)