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

2017/02/13 by Mounir Elloumi, Elloumi, Mounir, Janne-Kathrin Günther +3
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Mathematical Analysis and Transform Methods #math.RT

paper · pdf · doi:10.48550/arxiv.1702.03747

49 pages

arxiv created 2017/02/13 · arxiv updated 2017/02/14

Abstract

Let G_n=U(n)\ltimes \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^\ddagger /G_n of G_n . In this paper, we determine the topology of the space \mathfrak g_n^\ddagger /G_n and we show that the correspondence with \widehat G_n is a homeomorphism.

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