Let $Gsubsethat{G}$ be two complex connected reductive groups. We deals with the hard problem of finding sub-$G$-modules of a given irreducible $hat{G}$-module. In the case where $G$ is diagonally embedded in $hat{G}=Gtimes G$, S. Kumar and O. Mathie
u found some of them, proving the PRV conjecture. Recently, the authors generalized the PRV conjecture on the one hand to the case where $hat{G}/G$ is spherical of minimal rank, and on the other hand giving more sub-$G$-modules in the classical case $Gsubset Gtimes G$. In this paper, these two recent generalizations are combined in a same more general result.
