Abstract : Describing the Gelfand construction for the analytic states on an universal enveloping algebra, we characterize pure states and re-find the main result of a preceding work with L. Abdelmoula and J. Ludwig on the separation of unitary irreducible representations of a connected Lie group by their generalized moment sets.
Didier Arnal, Mohamed Selmi. Moment Map and Gelfand Transform for the Enveloping Algebra. Journal of Lie Theory, Heldermann Verlag, 2019, 29 (1), pp.227-237. ⟨hal-02173488⟩