# Reducibility tensor product representation

 P: 37 Hello everyone, Say I have two irreducible representations $\rho$ and $\pi$ of a group $G$ on vector spaces $V$ and $W$. Then I construct a tensor product representation $\rho \otimes \pi : G\to \mathrm{GL}\left(V_1 \otimes V_2\right)$ by $\left[\rho \otimes \pi \right] (g) v\otimes w = \rho (g) v \otimes \pi (g) w$. I now wish to know whether or not this representation is reducible or irreducible. If it cannot be determined, then I wish to know what further conditions imply reducibility or irreducibility. However, I have not been able to find an answer to this anywhere. Can anyone provide some insight? Thanks for any help.