Admissibility for a class of subgroups of the metaplectic group

Abstract

A class of subgroups of the symplectic group is introduced that take the form of a semidirect product arising from the action of a matrix group on a linear space. It is shown that the groups are isomorphic to subgroups of the affine group, and their metaplectic representation is equivalent to a sum of subrepresentations of the wavelet representation. Using this equivalence, admissibility conditions for the metaplectic representation are derived.