2014 Fiscal Year Final Research Report
Classification theory of visible actions on complex homogeneous spaces
Project/Area Number |
24740026
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Tokai University |
Principal Investigator |
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Project Period (FY) |
2012-04-01 – 2015-03-31
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Keywords | 代数学 / リー群の表現論 / 可視的作用 / スライス / カルタン分解 / 無重複表現 / 認容表現 |
Outline of Final Research Achievements |
The aim of our study is to construct a classification theory of visible actions on complex homogeneous spaces. In this study, we prove that for an affine complex homogeneous space of a complex simple Lie group the compact group action on it is visible if and only if it is spherical. During this study, we provide a generalization of a Cartan decomposition for a special case of Cayley type spherical homogeneous space and an explicit description of a submanifold which meets every orbit. Moreover, we give a characterization of a non-compact Hermitian symmetric space to be of non-tube by visible actions on it, the admissibility and the multiplicity-freeness of the restriction of (a scalar type) holomorphic discrete series representation.
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Free Research Field |
数物系科学
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