Timeline for From Weyl groups to Weyl groupoids?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2016 at 20:36 | vote | accept | Saal Hardali | ||
| Apr 30, 2016 at 19:29 | vote | accept | Saal Hardali | ||
| May 1, 2016 at 16:28 | |||||
| Apr 30, 2016 at 19:17 | answer | added | Ben Webster♦ | timeline score: 6 | |
| Apr 30, 2016 at 18:20 | answer | added | Uri Bader | timeline score: 4 | |
| Apr 30, 2016 at 16:00 | comment | added | Saal Hardali | @S.Carnahan That's great! Can I make this geometric? i.e. is there a weyl group torsor $W \to G/B \to G/T$ ? | |
| Apr 30, 2016 at 15:54 | comment | added | S. Carnahan♦ | I would normally choose morphisms to be automorphisms seen as elements of $GL(\mathfrak{g})$ instead of exponentials - this is not a big deal as long as you work over the real or complex numbers. To get a Weyl group, you consider a groupoid whose objects are Cartan subalgebras, together with the obvious functor from $\mathcal{W}$. Fibers are naturally W-torsors. | |
| Apr 30, 2016 at 15:54 | comment | added | Qiaochu Yuan | It's easier to have this discussion on the Lie group rather than Lie algebra level. There for $G$ a compact connected Lie group you can consider the groupoid whose objects are maximal tori and whose morphisms are conjugations. Every object in this groupoid is isomorphic, and all of their automorphism groups are the Weyl group. | |
| Apr 30, 2016 at 13:13 | history | edited | Saal Hardali |
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| Apr 30, 2016 at 13:06 | history | asked | Saal Hardali | CC BY-SA 3.0 |