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Defining manifolds and symmetries of nonlinear special functions in several variables

定义多变量非线性特殊函数的流形和对称性

基本信息

批准号：
13440054
负责人：
TAKANO Kyochi
金额：
$ 6.59万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2001
资助国家：
日本
起止时间：
2001 至 2004
项目状态：
已结题

项目摘要

1.We have constructed the defining manifolds of the Garnier system and all its degenerate systems in two varibales. We have also solved the same problem for the Noumi-Yamada system of type A^<(1)>_4.2.We have proved that the manifold defined by means of Backlund transformation group for each Painleve equation is isomorphic to the corresponding defining manifold constructed by K.Okamoto.3.We have shown that there exists an hierarchy in the Backlund transformation groups for Painleve equations, namely, the Backlund transformation groups for all Painleve equations can be obtained successively from that for the sixth Painleve equation by the use of the usual confluence procedures.4.We have characterized the Backlund transformation group for the sixth Painleve equation by means of Riemann-Hilbert correspondence, namely, the correspondence from the phase space(the space of initial conditions) of the sixth Painleve equation to the moduli space of the monodromy representation is just a covering mapping with the affine Weyl group of type D^<(1)>_4 as the covering transformation group.

1.构造了双变量加尼尔系统及其所有退化系统的定义流形。我们还解决了A^<(1)>_4.2型的Noumi-Yamada系统的相同问题。证明了用Backlund变换群对每个Painleve方程定义的流形与okamoto构造的相应定义流形同构。3 .我们证明了painlevel方程的Backlund变换群中存在层次关系，即使用通常的合流程序，可以由第六个painlevel方程的Backlund变换群依次得到所有painlevel方程的Backlund变换群。我们用Riemann-Hilbert对应刻画了第六Painleve方程的Backlund变换群，即第六Painleve方程的相空间（初始条件空间）到单态表示的模空间的对应只是以D^<(1)>_4型仿射Weyl群为覆盖变换群的覆盖映射。