Minimal and Maximal Semigroups Related to Causal Symmetric Spaces

Abstract

be an irreducible globally hyperbolic semisimple symmetric space, and let S⊆G be a subsemigroup containing H not isolated in S. We show that if So≠ 0 then there are H-invariant minimal and maximal cones Cmin⊆Cmax in the tangent space at the origin such that H exp Cmin⊆S⊆HZK(a)expCmax. A double coset decomposition of the group G in terms of Cartan subspaces and the group H is proved. We also discuss the case where G/H is of Cayley type.