2004 Fiscal Year Final Research Report Summary
Research on Orbits of Semisimple Lie Algebras and Representations
| Project/Area Number |
15540013
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | National University Corporation Tokyo University of Agriculture and Technology |
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Principal Investigator |
SEKIGUCHI Jiro National University Corporation Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Professor, 大学院・共生科学技術研究部, 教授 (30117717)
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| Co-Investigator(Kenkyū-buntansha) |
MAEDA Hironobu National University Corporation Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Associate Professor, 大学院・共生科学技術研究部, 助教授 (50173711)
MURO Masakazu Gifu University, Faculty of Engineering, Professor, 工学部, 教授 (70127934)
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| Project Period (FY) |
2003 – 2004
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| Keywords | Simple Lie algebra / nilpotent orbit / Weyl group / projective plane / c関数 / 対称空間 |
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| Research Abstract |
1.J.Sekiguchi studied the relation among the invariants of regular polyhedral groups, Appell's hypergeometric functions with special parameters and basic invariants of irreducible reflection groups of rank four. In particular, they find that basic invariants are so chosen that they are decomposed into two factors mod the quadratic invariant. And this decomposition is related with the degeneration of Appell's hypergeometric function. This work is a joint work with Mitsuo Kato.
2.J.Sekiguchi organized the conference (Conference on Nilpotent Orbits and Representation Theory 2004) held at Fuji-Sakura-So (September,2004) and at that time Professor D.Z.Djokovic reported the result of the joint work with Sekiguchi and Kaiming Zhao. This work is concerned with an action of general linear group on n by n matrices. In particular they showed that the nul-cone associated with this action is irreducible as an variety.
3.J.Sekiguchi studied simple eight-line arrangements with some conditions on a real projective plane. This is a joint work with Tetsuo Fukui. Their interest is related with the action of Weyl group of type E8. They first treat a diagram consisting of ten nodes similar to the Dynkin diagram and attach E8-roots to nodes. To each of such a diagram, it is possible to construct a simple arrangement of eight lines on a real projective plane. They showed that this correspondence is, in fact, a W(E8)-equivariant map. This solves a part of their conjecture.
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