A UNIFIED APPROACH TO CONCRETE PLANCHEREL THEORY OF HOMOGENEOUS SPACES

A new paradigm for concrete Plancherel analysis on homogeneous spaces is established wherein the distinction between finite and infinite mul tiplicity is de-emphasized. A unified treatment - incorporating the Pe nney-Fujiwara formulation for finite multiplicity and the Bonnet formu lation for infinite multiplicity - is presented. The heretofore unreco gnized similarities in the two theories are uncovered and emphasized. The unified theory is illustrated with explicit computations of the Pl ancherel formula for a certain class of homogeneous spaces of semidire ct product groups.