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Study of Representation theory and Combinatorics and their related topics

表示论和组合学及其相关主题的研究

基本信息

批准号：
09640059
负责人：
KOIKE Kazuhiko
金额：
$ 2.24万
依托单位：
AOYAMA GAKUIN UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640059/
关键词：
Classical Groups Young diagram Weyl groups commutative differential operators Dynamical systems Algebraic surface Geometric genus Computational mathematics q-analog 中心化群計算数論普遍指標

项目摘要

Koike showed that the Young-diagrammatic method is still effective for representation theory of the Spinor groups and the orthogonal groups of even ranks in describing the decomposition of the tensor products of two irreducible representations and the branching rules of the irreducible representations.This means that Young-diagrammatic method works well for all the classical groups : He published surveys of his study on representation theory of the classical groups in the Journal "Suugaku" (Publisher : Mathematical Society of Japan) and its English translation (Publisher : American Mathematical Society).Taniguchi showed that the higher terms of the commutative differential operator algebras whose elements are invariant under the action of the Weyl groups are uniquely determined by its second-degree part if the potentialfunction of the second-degree part is periodical. And also if the potential function of the second-degree part is rational, he gives a universal construction of the commutative differential algebras by using the Dunki operators.Yano published two books on the dynamical systems, which put emphasis on the geometric viewpoints. To help the readers understand easily, he focused on one and two dimensional phase spaces and explained the scheme of the important subjects such as Morse-Smale system and Anosov system etc. explicitly.Inoue gives two new methods of constructions of algebraic surfaces of general type whose geometric genus are. zero. Ihara improves his software "package for the multiple precision calculation of integers" and is working on developing a new software for number theory of the elliptic curves by using the above.

小池表明，杨图解法仍然是有效的表示理论的旋量群和正交群的偶数秩在描述分解的张量积的两个不可约表示和分支规则的不可约表示。这意味着杨图解法适用于所有的经典群体：他发表的调查，他的研究代表性理论的经典群体在杂志“Suugaku”（出版社：日本数学会）及其英文译本（发布者：Taniguchi证明了在Weyl群作用下元素不变的交换微分算子代数的高阶项唯一地由它的第二阶确定，如果二次部分的势函数是周期性的，则二次部分是周期性的。如果二次部分的势函数是有理的，他利用Dunki算子给出了交换微分代数的一个普遍构造。矢野发表了两本关于动力系统的书，其中强调了几何观点。为了帮助读者容易理解，他专注于一，二维相空间，并解释了该计划的重要课题，如Morse-Smale系统和Anosov系统等明确井上给出了两个新的方法建设代数曲面的一般类型，其几何属。零.井原改进了他的软件“整数的多精度计算软件包”，并正在利用上述软件开发一种新的椭圆曲线数论软件。