On the dual topology of the groups U(n)xH_n

Abstract

Let $G_n=U(n)⋉{\mathbb{H}}_n$ be the semi-direct product of the unitary group acting by automorphisms on the Heisenberg group ${\mathbb{H}}_n$. According to Lipsman, the unitary dual $\widehat{G_n}$ of $G_n$ is in one to one correspondence with the space of admissible coadjoint orbits ${\mathfrak{g}}_n^{‡}/G_n$ of $G_n$. In this paper, we determine the topology of the space ${\mathfrak{g}}_n^{‡}/G_n$ and we show that the correspondence with $\widehat{G_n}$ is a homeomorphism.

49 pages

References in corpus (1)

• The C*-algebra of SL(2,R)