Study on flag domains and its application to Hodge theory
| Project/Area Number |
16K17576
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Senshu University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 旗領域 / 対称空間 / リー理論 / 組み合わせ論 / リー群 / ルート系 / ワイル群 / 複素幾何 / 表現論 / リー代数 / ホッジ理論 / Mumford-Tate領域 / 複素代数幾何学 |
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| Outline of Final Research Achievements |
An open real group orbit in a complex flag manifold is called a flag domain. In this research project, we studied geometric properties of flag domains. One of the main result is about pseudoconcavity of flag domains. We proved that a flag domain is either pseudoconvex or pseudoconcave, which is positive confirmation of Huckleberry's conjecture. The paper on this result has been published in Mathematische Annalen as a co-authored paper with Huckleberry and Latif. Moreover, we studied cycle-connectivity of pseudoconcave flag domains. We determined which pseudoconcave flag domain is one-connected in some particular cases.
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| Academic Significance and Societal Importance of the Research Achievements |
この研究成果によりAlan Huckleberry氏が過去の論文で立てた予想が肯定的に解決され，旗領域に関する理解が進んだ．またその成果は国際研究雑誌に掲載され，様々な研究機関で講演を行った．
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Report
(5 results)
Research Products
(15 results)
