  Let $G$ be a real simple Lie group, $\got g$ its Lie algebra. Given a
nilpotent adjoint $G$-orbit $O$, the question is to determine the irreducible
unitary representations of $G$ that we can associate to $O$, according to the
orbit method. P.Torasso, in [22], gave a method to solve this problem if $O$ is
minimal. In this paper, we study the case where $O$ is any spherical nilpotent
orbit of $sl_n({\mathbb R})$, we construct, from $O$, a family of
representations of the two-sheeted covering of $SL_n({\mathbb R})$ with
Torasso's method and, finally, we show that all these representations are
associated to the corresponding orbit.
