2018 Fiscal Year Final Research Report
Orbit decomposition of multiple flag varieties
| Project/Area Number |
16K05084
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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 |
Algebra
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| Research Institution | Ryukoku University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 古典群 |
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| Outline of Final Research Achievements |
Let G be the split orthogonal group over an infinite field F of characteristic not two. We completely classified multiple flag varieties (direct products of flag varieties) of G of finite type. Here a multiple flag variety M is said to be of finite type when M has a finite number of G-orbits with respect to the diagonal action. This result was announced in arXiv:1903.06335 as a preprint and submitted to a journal.
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| Free Research Field |
リー群論
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| Academic Significance and Societal Importance of the Research Achievements |
この問題は一般線形群と symplectic 群のとき、および奇数次 split 直交群のときに解決されていた。今回の成果により、古典群のときの分類は完成した。また、体 F は任意であるので、さらに広い応用が期待される。
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