  For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we
give a characterization of the set of dominant integral weights $\lambda$ such
that for any rational point $\mu$ in the fundamental Weyl chamber,
$2\lambda-\mu$ is a non-negative rational combination of the simple roots if
and only if $V_{m\mu}\subseteq V_{m\lambda}\otimes V_{m\lambda}$ for some
positive integer $m$.
