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

For the classical groups (including $U(n)$, $SO(n)$, and $Sp(2n)$), let V be defining representation (the natural inclusion of $G$ into $GL(n,C)$), when are $S^kV$ and $Λ^kV$ irreducible ?

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 ?

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Symmetric and alternating powers of defining representation of classical groups

For the classical groups (including $U(n)$, $SO(n)$, and $Sp(2n)$), let V be defining representation (the natural inclusion of $G$ into $GL(n,C)$), when are $S^kV$ and $Λ^kV$ irreducible ?