Affordable Access

Access to the full text

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

Authors
  • Abdelmoula, Lobna1
  • Baklouti, Ali1
  • Bouaziz, Yasmine1
  • 1 Faculty of Sciences at Sfax, Street Soukra, 3000 , (Tunisia)
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.

Report this publication

Statistics

Seen <100 times