Let $V$ and $W$ be complex irreducible representations of $GL_n(F_q)$ where $F_q$ is finite field. Is the decomposition of $V \otimes W$ into irreducible representations known? ---------------- PS Same question: https://mathoverflow.net/questions/12377/decomposing-tensor-products-of-irreducible-representations-of-reductive-groups-o?rq=1