Timeline for orbit of a Dynkin diagram automorphism
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 11, 2011 at 0:47 | vote | accept | Binai | ||
| Jan 10, 2011 at 23:06 | comment | added | Jim Humphreys | @Chris: As Johannes points out, "orbit" refers to a group action. In any case, the explicit answer to your question requires some case-by-case enumeration and is rather easy, but see the further information given by Hugh Thomas for the folding process. | |
| Jan 10, 2011 at 22:03 | answer | added | Hugh Thomas | timeline score: 4 | |
| Jan 10, 2011 at 19:15 | comment | added | Johannes Hahn | "Orbit" should probably understood as the orbit of the group $\langle f\rangle$. | |
| Jan 10, 2011 at 18:17 | comment | added | Binai | @Jim: Thanks for the attention. My problem is exactly in understand the term "orbit" in this situation. What is your idea? I know that the explicit answer will not be obvious. But I am happy if someone give me an insight in what it can be! | |
| Jan 10, 2011 at 17:15 | comment | added | Jim Humphreys |
It's unclear to me what "orbit" means in this non-group context. Aside from that, the point of the question isn't obvious. For each relevant simple type, it's very easy to see what each such map does, using the explicit lists of roots in Bourbaki (for $E_6$ the table at the end of Springer's 1966 paper in IHES No. 30, available online through www.numdam.org, is convenient).
|
|
| Jan 10, 2011 at 15:22 | history | asked | Binai | CC BY-SA 2.5 |