On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces

Original · EN

Let S be a real-analytic hypersurface in Cⁿ or, more generally, a CR-submanifold in a complex manifold Z of arbitrary CR-codimension. This paper addresses the question, when a local biholomorphic map between open sets in Z sending an open piece of S into S extends to a global biholomorphic self-map of Z preserving S. We give answers for a large class of Levi-degenerate group orbits in compact Hermitian symmetric spaces.