Displaying similar documents to “On the complex and convex geometry of Ol'shanskii semigroups”

On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb (1999)

Annales de l'institut Fourier

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Let M = G / H be a real symmetric space and 𝔤 = 𝔥 + 𝔮 the corresponding decomposition of the Lie algebra. To each open H -invariant domain D 𝔮 ⊆ i 𝔮 consisting of real ad-diagonalizable elements, we associate a complex manifold Ξ ( D 𝔮 ) which is a curved analog of a tube domain with base D 𝔮 , and we have a natural action of G by holomorphic mappings. We show that Ξ ( D 𝔮 ) is a Stein manifold if and only if D 𝔮 is convex, that the envelope of holomorphy is schlicht and that G -invariant plurisubharmonic functions correspond to...