| Project/Area Number |
26610001
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University |
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Principal Investigator |
TERAO Hiroaki 北海道大学, 国際本部, 特任教授 (90119058)
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| Project Period (FY) |
2014-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 超平面配置 / ルート系 / ワイル配置 / 自由配置 / イデアル / 指数 / 高さ / 双対分割定理 / 代数学 / ワイル群 |
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| Outline of Final Research Achievements |
The main purpose of this research was to obtain new results, by applying the theory of hyperplane arrangements to the algebraic/geometric study of root systems or reflection groups in general, with a new depth which would not be reachable by the known approaches. The research began with explicit calculations with the intention to prove the first conjecture by Summers-Tymoczko in mind. Finally, we verified the dual partition theorem by Shapiro-Steinberg-Kostant-Macdonald, which is a celebrated theorem found in textbooks, for some restriction arrangements of the Weyl arrangements.
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