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On the generalized moment separability theorem for type 1 solvable Lie groups

  • Lobna Abdelmoula , Ali Baklouti EMAIL logo and Yasmine Bouaziz

Abstract

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G^, the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰(𝔤)*, the dual vector space of 𝒰(𝔤). The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by J(π). We say that G^ is generalized moment separable when the generalized moment sets differ for any pair of distinct irreducible unitary representations. Our main result in this paper provides a second proof of the generalized moment separability theorem for G.

MSC 2010: 22E27; 32G05

Funding statement: This work was completed with the support of D.G.R.S.R.T Research Laboratories: LR 11 ES 35 and LR 11 ES 52.

Acknowledgements

The authors are deeply grateful to the referee for useful comments and important suggestions which helped to improve the presentation of the paper.

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Received: 2017-04-03
Revised: 2017-11-28
Accepted: 2017-12-04
Published Online: 2018-02-17
Published in Print: 2018-10-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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