The theory of transformation groups and its application

变换群理论及其应用

• 批准号: 06452009
• 负责人: OKAMOTO Kazuo
• 金额: $ 4.16万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (B)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-06452009/
• 关键词: Integrable system; Deformation theory; Monodromy; Special functions; Hypergeometric functions; Painleve equations; Garnier systems; Birational canonical; 多変数特殊関数; ホロノミック; 梯子構造; 線型偏微分方程式系

The present project aimed studies on transformation groups, appearing in the various aspects of analysis. Investigating transformation groups of completely integrable systems defined in a complex domain, we obtaind a new point of view and various resultes particularly on this subject. The group of this project in the University of Tokyo concerned researchs on nonlinear integrable systems, in particular from the point of view of the algebraic theory. The main objects of our investigations is losted as follows :(1) Only special cases of partial differential equations admit fruitfull algebraic structure of their transformation groups. Since few of such equations, we attempt to construct the examples systematically.(2) We determine the transformation groups and their realization of nonlinear integrable system, in partcular these of the Garnier systems.(3) One of the most important points of studies on completely integrable systems is an application to theoretical physics. We try to establish the general method of determination of transformation groups of integrable systems.The investgators of this research project have continued their studies on transformation groups of integrable systems and announced their own results obtained during two years, 1994-95, in various occasins They have published some of results in journals.

本项目旨在研究变换群，出现在分析的各个方面。通过对复域上完全可积系统的变换群的研究，我们得到了一个新的观点和一些新的结果。东京大学的这一项目的研究小组关注非线性可积系统的研究，特别是从代数理论的角度。本文的主要研究内容如下：（1）只有偏微分方程的特殊情况才有其变换群的有效代数结构。由于这类方程很少，我们试图系统地构造例子。(2)确定了非线性可积系统的变换群及其实现，特别是Garnier系统的变换群及其实现。(3)研究完全可积系统的一个重要方面是在理论物理中的应用。本文试图建立确定可积系统变换群的一般方法，本课题的研究者们在1994-95年的两年时间里，继续对可积系统变换群的研究，并在各种场合公布了自己的结果，部分结果已在期刊上发表。

项目成果

折原明夫: "Isometries on the l'-sum of Co (Ω.E) type spaces" Journal of Math.Sciences,Univ.Tokyo. 2. 131-154 (1995)

Akio Orihara：“Co (Ω.E) 型空间的 l-sum 等距”，东京大学数学科学杂志，2. 131-154 (1995)。

Akio ORIHARA: "Isometries on the l^1-sum of C_0 (OMEGA, E)" J.Math.Sci.2. 131-154 (1995)

Akio ORIHARA：“C_0 (OMEGA，E) 的 l^1-sum 的等距”J.Math.Sci.2。

Kazuo OKAMOTO: "On the holonomic deformation of linear ordinary differential equations on an elliptic curve" Kyushu J.Math.49. 281-308 (1995)

Kazuo OKAMOTO：“椭圆曲线上线性常微分方程的完整变形”九州 J.Math.49。

林祥介: "A model of the entry of comet Shoemaker-Levy 9 into Jupiter's Atmosphere" Proc.of the 28th ISAS Lunar and Planetary Sym.1-13 (1995)

Shosuke Hayashi：“彗星 Shoemaker-Levy 9 进入木星大气层的模型”Proc.of the 28th ISAS Lunar and Planetary Sym.1-13 (1995)

S.NAKAJIMA: "On Gauss sum characters of finite groups and generalized Bernoulli numbers" J.Theorie des nombres de Bordaux. (1994)

S.NAKAJIMA：“论有限群的高斯和特征和广义伯努利数”J.Theorie des nombres de Bordaux。