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Dec 8, 2017 at 0:03 comment added Jim Humphreys Note that your Question 1 has a familiar answer, though Question 2 was dealt with much more recently in a precise way. (In general, it's best here to formulate a single question.)
Dec 8, 2017 at 0:01 answer added Jim Humphreys timeline score: 6
Dec 7, 2017 at 16:46 vote accept user148212
Dec 7, 2017 at 15:38 answer added Jay Taylor timeline score: 7
Dec 7, 2017 at 8:54 comment added user148212 @JayTaylor Thank you! This is very useful. Could you put this into an answer?
Dec 7, 2017 at 6:39 comment added Jay Taylor This is false for a general connected reductive algebraic group but is true if the group is simple and simply connected. This is discussed in Steinberg's "Endomorphisms of linear algebraic groups". Parametrising the simple modules in the general case is disussed by Brunat and Lübeck in the following paper arxiv.org/pdf/1211.3692.pdf.
Dec 7, 2017 at 6:00 history asked user148212 CC BY-SA 3.0