  In his paper 'Theta lifting for representations with non zero cohomlogy',
Jian-Shu Li proved that a certain kind of cohomological representations of
$U(a,b)$ is automorphic. In this paper, this result is generalized to a more
general class of cohomological representations of this group. It comes from the
fact that these cohomological representations are the image by the theta
correspondance of some representations obtained by cohomological induction. In
proving this theorem, we also prove some cases of Adams conjecture.
