| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| 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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