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

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We present a large class of homogeneous 2 -nondegenerate CR-manifolds M , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains U,V in M extends to a global real-analytic CR-automorphism of M . We show that this class contains G -orbits in Hermitian symmetric spaces Z of compact type, where G is a real form of the complex Lie group \mathsf{Aut}(Z)^{0} and G has an open orbit that is a bounded symmetric domain of tube type.