Study of invariants and various structure of symplectic quotients
| Project/Area Number |
24540093
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Chuo University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Shigeaki 中央大学, 理工学部, 教授 (60166212)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | シンプレクティック商 / 余随伴軌道 / 旗多様体 / ベクトル分割関数 / 超幾何関数 / ウェイト多様体 |
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| Outline of Final Research Achievements |
First, we obtained an explicit formula for a vector partition function with possibly negative weights. As an example, for the root system of type A, we obtain an alternative proof of certain formulas for the vector partition/volume function over the `nice chamber.' They are also applied to a presentation of solutions of a certain hypergeometric system. Second, we explicitly described the special multiple weight variety of type A as a tower of projective space bundles. Consequently, the cohomology ring of this space is written down in a very simple form. As an application, we obtained a system of differential equations which characterizes the special vector volume function of type A.
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Report
(4 results)
Research Products
(10 results)
