Study of Representation theory and Combinatorics and their related topics

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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.