Journal of Lie Theory

no. 1
Moment Map and Gelfand Transform for the Enveloping Algebra
Didier Arnal1; Mohamed Selmi2
1Institut de Mathématiques de Bourgogne, Université de Bourgogne, B. P. 47870, 21078 Dijon, France
2Laboratoire Physique Mathématique, Université de Sousse, Rue Lamine Abassi, 4011 H. Sousse, Tunisia
Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 227-237
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.
DOI: 10.5802/jolt.1055
Classification: 22D10, 22D20, 52A05
Keywords: Universal enveloping algebra, analytic states, moment set of a representation

Didier Arnal  1 ; Mohamed Selmi  2

1 Institut de Mathématiques de Bourgogne, Université de Bourgogne, B. P. 47870, 21078 Dijon, France
2 Laboratoire Physique Mathématique, Université de Sousse, Rue Lamine Abassi, 4011 H. Sousse, Tunisia 
Didier Arnal; Mohamed Selmi. Moment Map and Gelfand Transform for the Enveloping Algebra. Journal of Lie Theory, Volume 29 (2019) no. 1, pp. 227-237. doi: 10.5802/jolt.1055
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     year = {2019},
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