Let $G$ be a classical groups (including $\operatorname U(n)$, $\operatorname{SO}(n)$, and $\operatorname{Sp}(2n)$), and $V$ be the defining representation (the natural inclusion of $G$ into $\operatorname{GL}(n,C)$).  When are $S^kV$ and $\bigwedge\nolimits^kV$ irreducible ?