Séparation des orbites coadjointes d'un groupe exponentiel par leur enveloppe convexe

Looking to the separation of irreducible unitary representations of an exponential Lie group G through the image of their moment map, we propose here a new way: instead to extend the moment map to the universal enveloping algebra of G, we define a non linear mapping Φ from the dual of the Lie algebra g of G to the dual g^+∗ of a larger solvable group G⁺, and we extend the representation from G to G⁺, in such a manner that the corresponding coadjoint orbits in g^+∗ have distinct closed convex hull. This allows us to separate the irreducible unitary representations of G.