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Journal of Lie Theory 29 (2019), No. 1, 227--237
Copyright Heldermann Verlag 2019

Moment Map and Gelfand Transform for the Enveloping Algebra

Didier Arnal
Institut de Mathématiques de Bourgogne, Université de Bourgogne, B. P. 47870, 21078 Dijon, France

Mohamed Selmi
Laboratoire Physique Mathématique, Université de Sousse, Rue Lamine Abassi, 4011 H. Sousse, Tunisia

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.

Keywords: Universal enveloping algebra, analytic states, moment set of a representation.

MSC: 22D10, 22D20, 52A05

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