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Jun 14, 2013 at 3:49 vote accept Eric O. Korman
Jun 12, 2013 at 2:03 comment added Peter Samuelson Isn't the set where both matrices are diagonalizable an open set? Then since they commute they're simultaneously diagonalizable, and in this case the representation decomposes as desired. I'm not sure if this generalizes or not, though...
Jun 11, 2013 at 19:16 history edited John Wiltshire-Gordon CC BY-SA 3.0
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Jun 11, 2013 at 19:08 history answered John Wiltshire-Gordon CC BY-SA 3.0