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Aug 28 at 11:01 comment added user536506 I should have checked the G2 case myself. Thanks alot.
Aug 28 at 11:00 vote accept user536506
Aug 28 at 9:11 answer added Kenta Suzuki timeline score: 4
Aug 27 at 23:47 comment added Grant B. Still doesn't work: in type $G_2$ take $\beta=s_1s_2\theta=\alpha_2$ where $\theta$ is the highest root and $\alpha_2$ is the long simple root.
Aug 27 at 22:11 history edited user536506 CC BY-SA 4.0
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Aug 27 at 22:11 comment added user536506 Yes, good point! But that shouldn't really contradict what I'm after. I've tried to fix the formulation.
Aug 27 at 21:33 comment added Grant B. The answer to your second question is no; in type $C_2$ take $\beta=s_1s_2\theta = s_1\theta=\alpha_2$ where $\theta$ is the highest root and $\alpha_2$ is the long simple root.
Aug 27 at 20:59 history edited user536506 CC BY-SA 4.0
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Aug 27 at 20:00 history edited user536506 CC BY-SA 4.0
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S Aug 27 at 19:59 review First questions
Aug 28 at 0:24
S Aug 27 at 19:59 history asked user536506 CC BY-SA 4.0