2009 Fiscal Year Final Research Report
The Radon-Penrose transforms and infinite dimensional representation theory, and their applications to the global analysis on non-compact complex homogeneous spaces
| Project/Area Number |
18540070
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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 | The University of Tokyo |
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Principal Investigator |
SEKIGUCHI Hideko The University of Tokyo, 大学院・数理科学研究科, 准教授 (50281134)
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| Project Period (FY) |
2006 – 2009
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| Keywords | ペンローズ変換 / 半単純リー群 / ユニタリ表現 / 有界対称領域 / 複素多様体 / 積分幾何 / 概均質ベクトル空間 / 超幾何函数 |
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| Research Abstract |
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. I have extended my previous results (the case that the transformation groups are indefinite unitary groups) to non-tube domains of type AIII ([1]), and also found explicit branching laws of certain singular unitary representations with respect to symmetric pairs by using the Penrose transform.
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