
Journal of Lie Theory 21 (2011), No. 4, 885904 Copyright Heldermann Verlag 2011 Automorphism Groups of Causal Makarevich Spaces Soji Kaneyuki Sophia University, Chiyodaku, Tokyo 1028554, Japan kaneyuki@hoffman.cc.sophia.ac.jp 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 Gstructure. Based on this, we obtain the Liouvilletype 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. Keywords: Causal structure, Gstructure, Cartan geometry, Liouvilletype theorem, symmetric cone, causal Makarevich space. MSC: 17C37, 53C10, 53C15, 53C35, 32M15 [ Fulltextpdf (345 KB)] for subscribers only. 