Analysis of an algebraic structure of a degenerate Garnier system from a viewpoint of algebraic solutions

从代数解的角度分析简并卡尼尔系统的代数结构

• 批准号: 20540207
• 负责人: KAWAMUKO Hiroyuki
• 金额: $ 1.83万
• 依托单位: Mie University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540207/
• 关键词: ガルニエ系; 有理解; 代数解; 差分パンルヴェ方程式; モノドロミー保存変形; 差分ガルニエ系

(1) We consider degenerate Garnier systems G(3,1,1) (which is defined by H.Kimura) and G(5/2,1,1) (which is defined by H.Kawamuko), and find all rational solutions of each equation.(2) We consider degenerate Garnier system G(3,2) (which is defined by H.Kimura), and find all algebraic solutions of G (3,2).(3) By using the results (1) and (2), we show that there is no birational transformation between these systems.(4) We consider a third order Fuchsian differential equation which has three regular singular points on Riemann sphere, and show that the Schlesinger transformation is equivalent to a difference VI Painlev\'e equation. Moreover, we can define a difference Garnier system in a similar way.

(1)考虑退化Garnier系统G(3，1，1)(由H.Kimura定义)和G(5/2，1，1)(由H.Kawamuko定义)，求出每个方程的所有有理解。(2)考虑退化Garnier系统G(3，2)(由H.Kimura定义)，求G(3，2)的所有代数解。(4)我们考虑了黎曼球面上有三个正则奇点的三阶Fuchsian微分方程，证明了Schlesinger变换等价于差分VI Painlev方程。此外，我们还可以用类似的方法定义一个差分Garnier系统。

项目成果

半整数型ガルニエ系と, (3, 2)型ガルニエ系の有理解

半整数型卡尼尔系统和(3, 2)型卡尼尔系统的理解

• 发表时间: 2008
• 作者: Akira Hoshiga;Taiichi Nose;大塚浩史;川向洋之
• 通讯作者: 川向洋之

G(3,1,1)型ガルニエ系の有理解について

关于G(3,1,1)型卡尼尔系统的智能理解

• 发表时间: 2010
• 作者: H. Awata;B. Feigin and J. Shiraishi;山田澄生;大塚浩史;川向洋之
• 通讯作者: 川向洋之

On the Garnier System of Half-Integer Type in Two Variables

关于二变量半整数型卡尼尔系统

• 发表时间: 2009
• 期刊: FUNKCIALAJ EKVACIOJ 52
• 作者: T. Futamura;K. Kitaura;Y. Mizuta;Hiroyuki Kawamuko
• 通讯作者: Hiroyuki Kawamuko