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

Abstract

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.