The multiplicity function on exponential and completely solvable homogeneous spaces

Abstract

It has been shown recently that the same multiplicity function appears in direct integral decompositions of both induced and restricted representations on exponential solvable groups — that is, a generalized form of Frobenius Reciprocity is valid. Qualitative results on that multiplicity function in the completely solvable case are proven in this paper — namely, necessary and sufficient conditions for finiteness and boundedness are obtained. The proof uses techniques from ‘pseudo-algebraic geometry’.