Dual topology of the Heisenberg motion groups

Abstract

Let ℍn be the (2n + 1)-dimensional Heisenberg group, and let Tn be the n-dimensional torus acting on ℍn by automorphisms. In this paper, we describe the space of admissible coadjoint orbits of the Heisenberg motion group Gn = Tn ⋉ ℍn and we determine the topology of this space. We show that the bijection between the unitary dual Ĝn of Gn and its admissible coadjoint orbit space is a homeomorphism.