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Jun 6, 2014 at 20:16 comment added Will Sawin @BS. Yes, the minimum is -2.
Jun 6, 2014 at 18:57 comment added BS. I had amost the same idea, instead using the SU(3) maximal torus in $G_2$ (coordinates $\alpha$ and $\alpha+\beta$). But I think that the minimum trace is -2, not -5.
Jun 6, 2014 at 15:24 history edited David E Speyer CC BY-SA 3.0
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Jun 6, 2014 at 15:06 history answered David E Speyer CC BY-SA 3.0