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Jun 21, 2017 at 13:21 comment added Mikko Korhonen @JayTaylor: Thanks Jay! I was pretty sure this must be known, but I was never able to find a reference.
Jun 21, 2017 at 13:06 comment added Jay Taylor Just to point out that this appears as Proposition 14.17 in Digne--Michel's book "Representations of Finite Groups of Lie Type". The argument they give is along the same lines as yours.
Jun 21, 2017 at 12:35 vote accept D_S
Jun 21, 2017 at 11:18 history edited Mikko Korhonen CC BY-SA 3.0
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Jun 21, 2017 at 11:11 history answered Mikko Korhonen CC BY-SA 3.0