Square-Integrability of Induced Representations of Semidirect Products

We consider a semidirect product G=A×′H, with A abelian, and its unitary representations of the form where x0 is in the dual group of A, G0 is the stability group of x0 and m is an irreducible unitary representation of G0∩H. We give a new selfcontained proof of the following result: the induced representation is square-integrable if and only if the orbit G[x0] has nonzero Haar measure and m is square-integrable. Moreover we give an explicit form for the formal degree of .