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Reducibility tensor product representation 
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#1
May2613, 02:46 AM

P: 37

Hello everyone,
Say I have two irreducible representations [itex]\rho[/itex] and [itex]\pi[/itex] of a group [itex]G[/itex] on vector spaces [itex]V[/itex] and [itex]W[/itex]. Then I construct a tensor product representation [itex]\rho \otimes \pi : G\to \mathrm{GL}\left(V_1 \otimes V_2\right)[/itex] by [itex]\left[\rho \otimes \pi \right] (g) v\otimes w = \rho (g) v \otimes \pi (g) w [/itex]. 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. 


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