Tensor product of two irreducible representations is not irreducible [closed]
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I have seen that if $rho: G longrightarrow text{GL}_{mathbb{C}}(V)$ and $alpha: G longrightarrow text{GL}_{mathbb{C}}(W)$ are two irreducible representations of a finite grup $G$ , then its tensor product representation $rho otimes alpha: G longrightarrow text{GL}_{mathbb{C}}(V otimes W)$ is usually not irreducible. Can anyone tell me an example?
abstract-algebra group-theory finite-groups representation-theory examples-counterexamples
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edited Dec 11 '18 at 16:07
Batominovski
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