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Automorphism groups of the classical domains. I, II. (English) Zbl 0635.32022
In these two notes the author constructs the groups of all holomorphic automorphisms of bounded symmetric domains of type I, III and IV in E. Cartan’s classification. Since these domains are homogeneous, and a transitive group of holomorphic automorphisms is easily constructed, the main point of the proof boils down to the determination of the isotropy group K of a point 0 in the domain.

32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
32M05 Complex Lie groups, group actions on complex spaces