Research on geometry related to Weyl groups and root systems
| Project/Area Number |
20540066
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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 |
Geometry
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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, 大学院・工学研究院, 教授 (30117717)
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| Co-Investigator(Renkei-kenkyūsha) |
FUKUI Tetsuo 武庫川女子大学, 生活環境学部, 教授 (70218890)
NORO Masayuki 神戸大学, 大学院・理学研究科, 教授 (50332755)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | ワイル群 / ルート系 / 斎藤自由因子 / 対数的ベクトル場 / 一意化方程式 / 一意化微分方程式 / 鏡映群 / 特異点 / b-関数 / 捩じれのない積分可能接続 |
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| Research Abstract |
The zero set of the discriminant of an irreducible real reflection group is known to be a Saito free divisor. In this research project, we construct and classify Saito free divisors in a 3-dimensional affine space. Moreover we clarify the relationship between such divisors and families of deformations of simple curve singularities. As a next stage, we succeeded to construct systems of uniformization equations with singularities along such divisors and classified them. We also obtained some results of the structures of them. We could generalize these results to the case of complex reflection groups of rank three.
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Report
(4 results)
Research Products
(68 results)
