Timeline for Realizations and pinnings (épinglages) of reductive groups
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Mar 11, 2010 at 17:11 | vote | accept | user717 | ||
| Mar 10, 2010 at 2:16 | comment | added | Kim Morrison | Poor, beautiful, butterflies, pinned to the page. | |
| Mar 9, 2010 at 23:34 | answer | added | BCnrd | timeline score: 18 | |
| Mar 9, 2010 at 22:44 | comment | added | user717 | I'm looking forward to your answer, Brian. I also wonder why Springer did not even mention in his "notes" (where he refers to SGA) what the relation of his realizations to the SGA notions is. Even if it's obvious, it's a little bit frustrating for a beginner. [It was of course a mistake to mention just you as the author for the pseudo-reductive groups book. I just had you in mind because of a recent answer...] | |
| Mar 9, 2010 at 19:03 | comment | added | Kevin Buzzard | Morning Brian . | |
| Mar 9, 2010 at 17:06 | comment | added | BCnrd | I'll send an answer later. This question raises a very good point which should be addressed in the p-red book (the issue of defining $\phi_a$ for all roots $a$). It is certainly something I thought about during the writing of Appendix A.4 of the book. I will discuss with my co-authors about the cleanest way to handle it and get back to you. | |
| Mar 9, 2010 at 16:48 | history | edited | BCnrd | CC BY-SA 2.5 |
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| Mar 9, 2010 at 16:35 | history | edited | BCnrd | CC BY-SA 2.5 |
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| Mar 9, 2010 at 16:05 | comment | added | user717 | I could figure out that one can extend the "partial realization" on the base to a realization by conjugating with elements of the Weyl group and introducing additional coefficients (this is how the $p_{ir + js}$ are defined in SGA and this is probably what happens in 9.2.1 in Springer). But my understanding is far from complete yet, so any help is still welcome! :) | |
| Mar 9, 2010 at 11:12 | comment | added | Kevin Buzzard | The obvious exercise to do here is surely to let $G$ be $GL_3$, define $\phi_\alpha$ to be the obvious thing for $\alpha$ a simple root, and then attempt to define $\phi_\alpha$ for the other positive root and to see if there is any flexibility. What happens if you do this exercise? Alternatively you can just wait for Brian to wake up. | |
| Mar 9, 2010 at 10:47 | history | edited | user717 | CC BY-SA 2.5 |
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| Mar 9, 2010 at 10:33 | history | edited | user717 | CC BY-SA 2.5 |
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| Mar 9, 2010 at 10:28 | history | asked | user717 | CC BY-SA 2.5 |