| Project/Area Number |
16K05122
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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 | The University of Tokyo |
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Principal Investigator |
SEKIGUCHI Hideko 東京大学, 大学院数理科学研究科, 准教授 (50281134)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2020: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2019: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2018: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2016: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
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| Keywords | ペンローズ変換 / ユニタリ表現 / 有界対称領域 / 表現の分岐則 / 複素多様体 / リー群 / グラスマン多様体 / 積分幾何 |
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| Outline of Final Research Achievements |
I have been studying so called the Penrose transform, which originated in mathematical physics. My view point is based on representation theory of semisimple Lie groups, in particular, a geometric realization of singular (infinite-dimensional) representations via the Penrose transform. Our main concern is with the characterization of the image of the Penrose transform by means of a system of partial differential equations on the cycle space, e.g., a generalization of the Gauss-Aomoto-Gelfand hypergeometric differential equations to higher degree.
During this period, I have focused on the comparison of two indefinite Grassmannian manifolds, which are not biholomorphic to each other, but their Dolbeault cohomologies may have intimate relations.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は当該研究代表者が従前行ってきたペンローズ変換の研究に立脚し，それをさらに深化させ高次元の非コンパクトな複素多様体の上で無限次元表現の幾何的な解明を目指すものである。非コンパクトな複素多様体のコホモロジーは無限次元空間になり，その構造は十分に解明されているとはいえない。半単純リー群の無限次元表現論と積分幾何の手法を用いて，このコホモロジー空間をより精密に理解し，逆にパラメータが特異な場合の無限次元表現の未知の性質を幾何的にとらえるという挑戦的な課題に取り組んでいる。
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