Automorphism Groups of Causal Makarevich Spaces

S. Kaneyuki

Journal of Lie theory, Tome 21 (2011) no. 4, pp. 885-904

Résumé

The Shilov boundary M^- of an irreducible bounded symmetric domain D of tube type is a flag manifold of a simple Lie group G(D) of Hermitian type. M^- has a natural G(D)-invariant causal structure. By a causal Makarevich space, we mean an open symmetric orbit in M^- under a reductive subgroup of G(D), endowed with the causal structure induced from that of the ambient space M^-. All symmetric cones in simple Euclidean Jordan algebras fall into the class of causal Makarevich spaces. We associate a causal structure with a certain G-structure. Based on this, we obtain the Liouville-type theorem for the causal structure on M^-, asserting the unique global extension of a local causal automorphism on M^-. By using this, we determine the causal automorphism groups of all causal Makarevich spaces.

Détail

Classification : 17C37, 53C10, 53C15, 53C35, 32M15
Mots-clés : Causal structure, G-structure, Cartan geometry, Liouville-type theorem, symmetric cone, causal Makarevich space