Timeline for Representations of reductive groups over arbitrary fields
Current License: CC BY-SA 2.5
5 events
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| Nov 19, 2010 at 23:40 | comment | added | Jim Humphreys | P.S. Looking again at the actual paper, I realize that in Section 6 there are quite a few examples. But the examples as well as the general theorems get technical, so it's not easy at first to extract the information in Kevin's concise answer. | |
| Nov 19, 2010 at 19:24 | comment | added | Jim Humphreys |
My recollection of Tits' paper is that he doesn't provide abundant examples, though as Brian says there should be negative answers to the question. Indeed, it would be very surprising in this general context for the answer always to be yes. Meanwhile, a very minor notational comment: most people use $\overline{k}$ for an algebraic closure and $k_s$ for a separable closure.
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| Nov 19, 2010 at 19:20 | answer | added | Kevin Buzzard | timeline score: 3 | |
| Nov 19, 2010 at 19:12 | comment | added | BCnrd | This looks identical to the analogous situation for absolutely irreducible representations of finite groups, where Schur's Lemma yields a Brauer obstruction to descending the field of definition to that of the character. (Serre's book on finite group representations gives many examples where the Brauer obstruction is nontrivial over interesting $F$.) In that spirit, there should be lots of examples where the answer is negative. | |
| Nov 19, 2010 at 18:05 | history | asked | anonymous | CC BY-SA 2.5 |