2019 Fiscal Year Final Research Report
Study on symplectic quotients concerned with branching problems
| Project/Area Number |
16K05137
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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) |
三好 重明 中央大学, 理工学部, 教授 (60166212)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | シンプレクティック商 / 余随伴軌道 / 旗多様体 / ウェイト多様体 / 分岐問題 / 凸多面体 |
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| Outline of Final Research Achievements |
We studied the multiplicity varieties and multiple weight varieties associated with coadjoint orbits (flag manifolds) of a compact Lie group, and obtained the results as follows.
First, we characterized the special vector volume function of type A, by means of a system of differential equations (arXiv: 1904.05000). Second, we proved that the symplectic volume function of a nondegenerate multiple weight variety of type A determines the cohomology ring over real numbers, and applied it to the study of double weight varieties of type A2. Third, we showed that a nondegenerate special weight variety of type A has the structure of a generalized Bott tower.
We gave presentations about the results as above in some international and domestic conferences.
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| Free Research Field |
位相幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
意味のあるよいクラスの空間の組織的構成、それらの各種不変量の決定と同型類や大域的構造の深い理解、またその過程における表現論や組合せ論への寄与、等が、学術的意義として挙げられる。また、個々の具体例における詳細な計算過程や計算結果自体にも味わいがある点は、本研究の特色・独創性の一つと考えられる。
さらに、国内外の他の研究との関連が判明し、派生する問題もいくつか得られたことは、今後の研究の広がりを示唆している。
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