ORBITAL SYMMETRIC SPACES AND FINITE MULTIPLICITY

摘要

It is proven that any algebraic symmetric space has finite multiplicity. The multiplicity is then shown to be bounded provided 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 be irreducible. (C) 1996 Academic Press, Inc. [References: 24]