Let G be a simply connected nilpotent Lie group,  be the finite-dimensional Lie algebra of G,  be a finite-dimensional vector space over  or  and  be the space of linear operators of  into  the Lie algebra of endomorphisms of  In this work, we construct a representation of G in  denoted by Ad^# a generalization of coadjoint representation of G, and extend the orbit method to the space 

polarization at an linear operator, induced representation, the orbit method, #-coadjoint representation, #-coadjoint orbit.