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Journal of the European Mathematical Society


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Volume 8, Issue 3, 2006, pp. 465–490
DOI: 10.4171/JEMS/63

Published online: 2006-09-30

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

W. Kaup[1] and Dmitri Zaitsev[2]

(1) Universität Tübingen, Germany
(2) Trinity College, Dublin, Ireland

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 $\Aut(Z)^{0}$ and $G$ has an open orbit that is a bounded symmetric domain of tube type.

Keywords: Hermitian symmetric spaces, tube domains, Jordan algebras, CR-equivalence problems, $2$-nondegenerate CR-manifolds

Kaup W., Zaitsev Dmitri: On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces. J. Eur. Math. Soc. 8 (2006), 465-490. doi: 10.4171/JEMS/63