A characterization of non-tube type Hermitian symmetric spaces by visible actions

作者：Sasaki Atsumu^*

来源：Geometriae Dedicata, 2010, 145(1): 151-158.

DOI：10.1007/s10711-009-9412-z

• Visible actions
• Complex manifold
• Slice
• Anti-holomorphic involution
• Multiplicity-free representations
• Hermitian symmetric space
• Tube type domain

Let G/K be an irreducible Hermitian symmetric space of non-compact type, and G(C)/K(C) its complexification by forgetting the original complex structure. Then, D := G(C)/[K(C), K(C)] is a non-symmetric Stein manifold. We prove that a maximal compact subgroup of G(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.

• 出版日期2010-4