Orbital Symmetric Spaces and Finite Multiplicity

It is proven thatanyalgebraic symmetric space hasfinitemultiplicity. The multiplicity is then shown to beboundedprovided that is the case for reductive symmetric spaces (a widely-believed, but as yet unproven fact). The method of proof involves an amalgamation of the Mackey Machine and the Orbit Method. A necessary and sufficient orbital condition is also derived for the quasi-regular representation of a symmetric space to beirreducible.