2006 Fiscal Year Final Research Report Summary
Actions of semisimple groups and Weyl groups and research on representations
| Project/Area Number |
17540013
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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 | Tokyo University of Agriculture and Technology |
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Principal Investigator |
SEKIGUCHI Jiro Tokyo University of Agriculture and Technology, Institute of Symbiotic Science and Technology, Professor, 大学院共生科学技術研究院, 教授 (30117717)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUI Tetsuo Mukogawa Women's University, School of Human Environmental Science, Professor, 生活環境学部, 教授 (70218890)
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| Project Period (FY) |
2005 – 2006
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| Keywords | root systems / configurations lines / Weyl group / vector fields / finite prime field / projective plane |
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| Research Abstract |
We obtained the following results on this research.
(1)J.Sekiguchi and T.Fukui studied the relationship between configurations of systems of eight lines on a real projective plane and the root system of type E8. We first defined a map of the totality of sets of 10 roots of the root system of type E8 with some conditions to the set of connected components of the configurations with certain conditions. Moreover we showed that this map is W(E8)-equivariant. Then we proved that there are 2160 number of orbits of such connected components by the action of the symmetric group of 8th degree. T.Fukui gave a talk on this result at the occasion of 12th International conference on Applications of Computer Algebra. Moreover we wrote a paper on this result and submitted it to Serdical Journal of Computing.
(2) The head investigator(Sekiguchi) classified Lie albegras generated by three vectors fields on three dimensional affines space with polynomial coefficients with some conditions. He gave talks at the occasions of RFBR-JSPS Joint symposium(Geometry and Analysis on Complex Algebraic Varieties) held in Moscow and Krasnoyarsk (Russia). He extended the results to the case of some of exceptional singularities due to Arnold and gave a talk at the RFBR-JSPS Joint symposium at RIMS, Kyoto University.
(3)J.Sekiguchi studied the action of Weyl group of type E6 on the set of configurations of systems of six lines on a projective plane over a finite prime field. He gave talks at the occasions of International conference (Algebraic Combinatorics) held at Sendai and a small workshop on Sendai number theory and algebraic combinatorics.
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Research Products
(2 results)
