A characterization of non-tube type Hermitian symmetric spaces by visible actions |
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Authors: | Atsumu Sasaki |
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Institution: | 1.Department of Mathematics, Faculty of Science and Engineering,Waseda University,Tokyo,Japan |
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Abstract: | Let G/K be an irreducible Hermitian symmetric space of non-compact type, and
G\mathbbC/K\mathbbC{G_{\mathbb{C}}/K_{\mathbb{C}}} its complexification by forgetting the original complex structure. Then,
D :=G\mathbbC/K\mathbbC, K\mathbbC]{D :=G_{\mathbb{C}}/K_{\mathbb{C}}, K_{\mathbb{C}}]} is a non-symmetric Stein manifold. We prove that a maximal compact subgroup of
G\mathbbC{G_{\mathbb{C}}} acts on D in a strongly visible fashion in the sense of Kobayashi (Publ Res Inst Math Sci 41:497–549, 2005) if and only if G/K is of non-tube type. Our proof uses the theory of multiplicity-free representations and a construction of a slice and an
anti-holomorphic involution on D. |
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