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Journal of Lie Theory 21 (2011), No. 4, 885--904
Copyright Heldermann Verlag 2011

Automorphism Groups of Causal Makarevich Spaces

Soji Kaneyuki
Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan

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.

Keywords: Causal structure, G-structure, Cartan geometry, Liouville-type theorem, symmetric cone, causal Makarevich space.

MSC: 17C37, 53C10, 53C15, 53C35, 32M15

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