权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

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.给出了与经典根系统有关的完全可积量子系统分类的一个猜想，并在适当的条件下证明了这一猜想。特别地，如果系统在无穷大点处有正则奇点，则分类是完全的，这是最重要的情况。明确地给出了对应于可积薛定谔算子的高阶算子，并证明了其完全可积性。系统之间的关系是明确的。约化李代数的标量型广义Verma模的零化子的生成元由初等因子的量化和线性代数中的极小多项式的量化两种方法构造。它们对应于Capelli恒等式和华氏算子的推广。给出了广义旗形上退化级数表示的微分方程及其在积分几何中的一些应用，包括Radon变换和Poisson变换。得到了退化级数的Whittaker模型存在的条件，并在代数意义下和适度增长条件下计算了实现的重数。给出了K-有限向量在实现中所满足的微分方程式，并得到了这些向量可以用经典的Whittaker函数来表示的条件。研究了一类比具有正则奇点的偏微分方程组稍宽的一般理论，并构造了其多值全纯解。对根系的各个子系统进行了分类，并对各子系统之间的同态进行了分类。研究了Heckman-Opdam超几何系统的合流极限、奇异集的限制以及不同实数形式的超几何系统。证明了利用Heckman-Opdam超几何函数的这个极限，可以得到具有适度增长的Whittaker向量。

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

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

Annihilators of generalized Verma modules of the scalar type for class Lie algebra

类李代数标量型广义 Verma 模的歼灭子

DOI：
发表时间：
2007
期刊：
Lecture Notes Series, National University of Singapore 12
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
通讯作者：
Toshio Oshima

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

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