Classification theory of visible actions on complex homogeneous spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24740026
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokai University
• Principal Investigator: SASAKI Atsumu 東海大学, 理学部, 講師 (60514453)
• Project Period (FY): 2012-04-01 – 2015-03-31
• 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.

Free Research Field

数物系科学