Institute of Engineering Division of Mathematical Sciences
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| | | Faculty of Engineering Department of Mechanical Systems Engineering | | Graduate School of Engineering Department of Mechanical Systems Engineering |
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| [ Education and Research Outline ] |
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| | | Structure of semisimple Lie groups and their representations,Saito free divisors and related topics |
| | I study Mathematics. A Lie group is a kind of generalizations of linear algebra. It is a group and a differentiable manifold. My main subject is structue of spaces assoiated with semisimple Lie groups. Many things about the structure of semisimple groups are known by their root systems. The ''root'' inspires the roots of algebraic equations. The name ''root' comes from the roots of the characterisitic equation of a matrix. And the root system is obtained by generalizing the properties of roots of a characteristic equation.
The Weyl group is defined as a finite group generated by reflections with respect to the root vectors. Studying the properties of Weyl groups, I am focused on various interesting phenomena. On the other hand, I also study nilpotent elements of semisimple Lie algebras. Many mysterious phenomena appear from the study of nilpotent orbits. I am studying these subjects for many years. Recent interest is Saito free divisors and related topics. In particular I am interested in the construction of systems of uniformization equations with respect to Saito free divisors. |
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| | | semisimple Lie algebra, symmetric space, Weyl group, nilpotent element, Saito free divisors, reflection groups, uniformization equation |
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| | | 1974 Graduated Faculty of Science, Tokyo Institute of Technology | | 1976 Completed Mazzsster course, Graduate School, Division of Natural Science, Nagoya University | | 1978 Withdrawn before completion Doctor course, Graduate School, Division of Natural Science, Kyoto University |
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| [ Field of specialization ] |
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| | | Saito free divisor, isolated singularity of hypersurface, root system, uniformization equations |
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| | Saito free divisors and related topics 2005/01-2010/12 [KEYWORD(S):Saito free divisor, root system, reflection group, uniformization equations]
Summary:Construction of Saito free divisors including those defined by discriminants of reflection groups, relations between root sytems, construction of uniformization equations with respect to Saito free divisors | Mathematical Study on Zalgaller polyhedra [KEYWORD(S):]
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