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Given a complex simple Lie algebra $\mathfrak{g}$ and a positive integer$\ell$, under the assumption $\lambda\gg\mu$, we show that irreduciblerepresentations of $\mathfrak{g}$ of the form $V(\lambda +w\mu)$, $w\in W,$with level at most $\ell$ appear in the fusion product of $V(\lambda)$ and$V(\mu)$. This verifies the existence of PRV components for the fusion productin this special case.

PRV for the Fusion product, the case $\lambda\gg\mu$