Using a parametrization for the universal covering O-0 of any coadjoin
t orbit O of a solvable (connected and simply connected) Lie group G,
we prove that the Moyal product on O-0 gives a realization of the unit
ary representations canonically associated to the orbit O in Pukanszky
's theory by deformation of the algebra of C-infinity functions on O-0
. By restriction to the standard covering O, we describe a structure o
f algebra on L(2)(O) and an adapted Fourier transform for type I group
G. (C) 1995 Academic Press, Inc.