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On q-Gamma and q-Bessel Functions Read chapter Read first chapter

2017 | OriginalPaper | Chapter

On the Dual Topology of the Groups \(\mathbf {U(n)\ltimes \mathbb H_n}\)

Authors : Mounir Elloumi, Janne-Kathrin Günther, Jean Ludwig

Published in: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

Publisher: Springer International Publishing

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Abstract

Let \(G_n=U(n)\ltimes H_n \) 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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Appendix
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Metadata
Title
On the Dual Topology of the Groups
Authors
Mounir Elloumi
Janne-Kathrin Günther
Jean Ludwig
Copyright Year
2017
Book
Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

Print ISBN: 978-3-319-65180-4

Electronic ISBN: 978-3-319-65181-1

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-65181-1_2

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