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On the holomorphic structure of \(G\)-orbits in compact Hermitian symmetric spaces. (English) Zbl 1136.32007
Summary: For every irreducible bounded symmetric domain \(D\) we are interested in the Cauchy-Riemann structure of the orbits under the real Lie group \(G = \operatorname{Aut}(D)\) in the compact Hermitian dual \(Z\) of \(D\). For orbits of this type we solve the CR-equivalence problem, compute explicitly their CR-automorphism groups and determine maximal holomorphic extendibility for continuous CR-functions and infinitesimal CR-transformations. The treatment is based on the Jordan-theoretic approach and some recent results by the author and D. Zaitsev [Invent. Math. 153, No. 1, 45–104 (2003; Zbl 1027.32032)].

32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
17C50 Jordan structures associated with other structures
32V05 CR structures, CR operators, and generalizations
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