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On invariant domains in certain complex homogeneous spaces. (English) Zbl 0881.32015

Summary: Given a compact connected Lie group \(K\). For a relatively compact \(K\)-invariant domain \(D\) in a Stein \(K^\mathbb{C}\)-homogeneous space, we prove that the automorphism group of \(D\) is compact and if \(K\) is semisimple, a proper holomorphic self mapping of \(D\) is biholomorphic.

MSC:

32M10 Homogeneous complex manifolds
32H35 Proper holomorphic mappings, finiteness theorems
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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