Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in , the unitary dual of G, sends smooth vectors of the representation space of π to , the dual vector space of . The convex hull of the image of the generalized moment map for π is called its generalized moment set, denoted by . We say that 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.
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.
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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