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

Authors
  • Abdelmoula, Lobna
  • Baklouti, Ali
  • Bouaziz, Yasmine
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Feb 17, 2018
Volume
9
Issue
4
Pages
247–277
Identifiers
DOI: 10.1515/apam-2018-0020
Source
De Gruyter
Keywords
License
Yellow

Abstract

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for Ο€ in G ^ {\widehat{G}} , the unitary dual of G, sends smooth vectors of the representation space of Ο€ to 𝒰 ⁒ ( 𝔀 ) * {{\mathcal{U}(\mathfrak{g})}^{*}} , the dual vector space of 𝒰 ⁒ ( 𝔀 ) {\mathcal{U}(\mathfrak{g})} . The convex hull of the image of the generalized moment map for Ο€ is called its generalized moment set, denoted by J ⁒ ( Ο€ ) {J(\pi)} . We say that G ^ {\widehat{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.

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