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This is actually a math question but I am looking for a physicist-friendly explanation. Consider two pseudo-real reps $D_1$ and $D_2$ of simple Lie groups $G_1$ and $G_2$, respectively. Why is $D_1\otimes D_2$ a real rep for $G_1\times G_2$?

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Related: math.stackexchange.com/q/243164/11127 –  Qmechanic May 1 '13 at 15:38
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