2011 Fiscal Year Final Research Report
Study of global structure and invariants of symplectic quotients
| Project/Area Number |
21540094
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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 | 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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| Co-Investigator(Renkei-kenkyūsha) |
OCHIAI Hiroyuki 九州大学, 数理(科)学研究科(研究院), 教授 (90214163)
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| Project Period (FY) |
2009 – 2011
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| Keywords | シンプレクティック商 / 運動量写像 / 余随伴軌道 / ベクトル分配関数 / 超幾何関数 / 多重ウェイト多様体 |
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| Research Abstract |
First, we showed that for any compact Lie group, the asymptotic dimension of the invariant subspace in the Weyl module is proportional to that of the invariant subspace in the multiple tensor product. Second, we obtained a formula for the asymptotic behavior of a vector partition function with possibly negative weights, which generalizes a known formula for a vector partition function without weights. Third, we introduced the notion of a multiple weight variety, and obtained a formula for its volume under certain assumptions.
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