Realization of symmetric spaces of Cayley type. (Réalisation des espaces symétriques de type Cayley.) (French. Abridged English version) Zbl 0839.53035

Let \(D= G/K\) be a Hermitian symmetric domain of tube type, isomorphic (via the Cayley transform c) to the tube domain \(V+i\Omega\), where \(V\) is a formally real Jordan algebra and \(\Omega\) the associated symmetric cone. Denote by \(G(\Omega)\) the identity component of the group of linear automorphisms of \(\Omega\) and \(H= c^{-1} G(\Omega)c\).
It is shown that the pseudo-Riemannian symmetric space \(G/H\) can be realized as an open dense subset of \(S\times S\), where \(S\) is the Shilov boundary of \(D\). Moreover, \(G/H\) is a globally causal space and the associated semigroup is characterized.
Proofs use mostly the theory of semisimple Jordan algebras.
Reviewer: G.Roos (Poitiers)


53C35 Differential geometry of symmetric spaces
17C36 Associated manifolds of Jordan algebras
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)