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

On components of the tensor square of a Weyl module