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

الأصل · EN

Let Gₙ=U(n) Hₙ be the semi-direct product of the unitary group acting by automorphisms on the Heisenberg group Hₙ. According to Lipsman, the unitary dual Gₙ of Gₙ is in one to one correspondence with the space of admissible coadjoint orbits gₙ /Gₙ of Gₙ. In this paper, we determine the topology of the space gₙ /Gₙ and we show that the correspondence with Gₙ is a homeomorphism.