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**Lockdown** Hi everyone,

Say I have two irreducible representations $\displaystyle \pi_1$ and $\displaystyle \pi_2$ of some group $\displaystyle G$ on vector spaces $\displaystyle V_1$ and $\displaystyle V_2$ and I form a tensor product representation

$\displaystyle \pi_1 \otimes \pi_2 : G \to \mathrm{GL}\left(V_1\otimes V_2\right)$

with $\displaystyle \left[\pi_1 \otimes \pi_2 \right]\left(g\right) v_1 \otimes v_2 = \pi_1 \left(g\right)v_1 \otimes \pi_2 \left(g\right) v_2$.

Under what conditions is this tensor product representations reducible or irreducible?

Thanks for any help on this!