Study of Representation theory and Combinatorics and their related topics

Koike证明了young -图解方法在描述两个不可约表示的张量积的分解和不可约表示的分支规则时仍然是有效的，它适用于旋量群和偶数秩正交群的表示理论。这意味着young -图解法适用于所有经典群：他在《Suugaku》杂志（出版商：日本数学学会）及其英文译本（出版商：美国数学学会）上发表了他对经典群的表征理论研究的调查。Taniguchi证明了元素在Weyl群作用下不变的交换微分算子代数的高项是由它的二阶部分唯一确定的，如果二阶部分的势函数是周期的。并且如果二阶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般构造。矢野出版了两本关于动力系统的书，强调了几何视点。为了便于读者理解，他着重于一维和二维相空间，并对Morse-Smale系统和Anosov系统等重要课题的方案作了明确的说明。Inoue给出了构造几何属为的一般型代数曲面的两种新方法。零。Ihara改进了他的软件“整数的多重精度计算包”，并利用上述方法开发了一个新的椭圆曲线数论软件。

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.