Systems of differential equations with group actions and their applications

具有群作用的微分方程组及其应用

基本信息

批准号：
16340034
负责人：
OSHIMA Toshio
金额：
$ 10.75万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

项目摘要

1. A conjecture for the classification of completely integrable quantum systems related to classical root systems is given and it is proved under a suitable condition. In particular the classification is complete if the systems have a regular singularity at an infinite point, which are most important cases. Higher order operators corresponding to the integrable Schrodinger operators are explicitly given and the complete integrability is proved. The relation between the systems are cleared.2. The generators of the annihilator of a generalized Verma module of a scalar type for reductive Lie algebra are constructed in two ways by quatization of elementary divisors and by that of minimal polynomials in linear algebra. These correspond to generalization of Capelli identity and Hua operators. These also give the differential equations for degenerate series representations on generalized flag manifolds and some applications to integral geometry including Radon and Poisson transformations.3. The condition for the existence of Whittaker model for degenerate series is obtained and the multiplicity of the realization is calculated under algebraic sense and also under the moderate growth condition. The differential equations satisfied by K-finite vectors in the realization is also obtained and the condition that the vectors are expressed by classical Whittaker functions is obtained.4. A general theory of systems of partial differential equations of a little wider class than those with regular singularities is studied and their multi-valued holomorphic solutions are constructed.5. The subsystems of a root system are classified and the homomorphisms between subsystems are classified.6. Confluent limits, restrictions to singular sets and different real forms of Heckman-Opdam hypergeometric systems are studied. It is proved that the Whittaker vector with the moderate growth is obtained by this limit of Heckman-Opdam hypergeometric function.

1。给出了与经典根系相关的完全集成量子系统分类的猜想，并在适当的条件下证明了这一点。特别是，如果系统在无限点处有规则的奇异性，这是最重要的情况，则分类是完整的。明确给出了与可集成的Schrodinger运算符相对应的高阶操作员，并证明了完整的集成性。清除系统之间的关系2。标量类型的广义VERMA模块的歼灭者的发电机通过两种方式构建基本除数和线性代数中的最小多项式。这些对应于Capelli身份和HUA操作员的概括。这些还提供了对通用标志歧管上的退化级数表示的微分方程，以及在包括ra和泊松变换（包括ra和泊松转换）的积分几何形状上的某些应用。3。获得了退化序列的惠特克模型的条件，并在代数意义和中等生长条件下计算实现的多样性。还获得了k-finite向量在实现中满足的微分方程，并获得了向量通过经典的惠特克函数表达的条件4。研究了比定期奇异性的偏差级别方程式系统的一般理论，并构建了它们的多值全态解决方案。5。根系的子系统被分类，并将子系统之间的同态分类。6。研究了汇合极限，对单数集的限制以及heckman-Opdam超几何系统的不同形式。事实证明，具有中等生长的惠特克向量是通过Heckman-Opdam超几何函数的这种限制获得的。

项目成果

期刊论文数量（88）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Radon transforms on generalized flag, manifolds

氡气在广义旗、流形上的变换

DOI：
发表时间：
2006
期刊：
影响因子：
0
作者：
KAWANO;Shuichi;et. al.;T. Oshima
通讯作者：
T. Oshima

線形代数の量子化と積分幾何

线性代数中的量化和积分几何

DOI：
发表时间：
2005
期刊：
数理解析研究所講究録 1421
影响因子：
0
作者：
H.Oda;T.Oshima;大島利雄
通讯作者：
大島利雄

Whittaker models of degenerate principal series

简并主级数 Whittaker 模型

DOI：
发表时间：
2006
期刊：
影响因子：
0
作者：
HYAKUTAKE;Hiroto;et. al.;大島利雄
通讯作者：
大島利雄

Completely integrable quantum systems associated with classical root systems

与经典根系统相关的完全可积量子系统

DOI：
发表时间：
2007
期刊：
SIGMA 3-061
影响因子：
0
作者：
H.Boos;M.Jimbo;T.Miwa;F.Smirnov;Y.Takeyama;B.Feigin et al.;H.Boos et al.;T. Oshima;T. Oshima;T. Oshima;T. Oshima;T. Oshima;T. Oshima;T. Oshima;Toshio Oshima;Toshio Oshima;Toshio Oshima;Toshio Oshima
通讯作者：
Toshio Oshima

Connection problems on Fuchsian ordinary differential equations

Fuchsian 常微分方程的连接问题

DOI：
发表时间：
2007
期刊：
影响因子：
0
作者：
H.Oda;T.Oshima;大島利雄;T. Oshima;T. Oshima;T. Oshima;T. Oshima;T. Oshima;T.Oshima;T.Oshima;Toshio OSHIMA;大島利雄;T. Oshima;大島利雄;T. Oshima;大島利雄;T. Oshima;大島利雄;T. Oshima;大島利雄;T. Oshima;大島利雄;T. Oshima
通讯作者：
T. Oshima