∗ products and representations of nilpotent groups

Abstract

On each orbit W of the coadjoint representation of a nilpotent, connected and simply connected Lie group G, there exist * products which are relative quantizations for the Lie algebra g of G. Choosing one of these * products, we first define a * -exponential for each X in g. These * -exponentials are formal power series and, with the * product, they form a group. Thanks to that, we are able to define a representation of G in a " * polarization" and to intertwine it with the unitary irreducible one associated to W. Finally, we study the uniqueness of our construction.