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