Timeline for Root systems and subroot systems
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 17, 2022 at 12:32 | comment | added | Callum | For a full classification check out this paper by Oshima which goes through it pretty extensively. | |
| Jun 17, 2022 at 12:31 | comment | added | Callum | @PSHINH2 note that just extending by the lowest root won't get you all possibilities except for ADE diagrams for the others (BCFG) you need to also allow extending by the lowest short root (see the answer here ) | |
| Jun 16, 2022 at 16:46 | comment | added | Sam Hopkins | You can find the highest root using “Kostant’s game” as discussed here: mathoverflow.net/a/172033/25028 | |
| Jun 16, 2022 at 16:44 | comment | added | PSHINH2 | @LSpice I have not, I will take a look. Thank you. | |
| Jun 16, 2022 at 16:39 | comment | added | LSpice | Have you looked in Carter's article on conjugacy classes in Weyl groups? I doubt he explicitly describes exactly what you want, but his computations might be relevant. | |
| Jun 16, 2022 at 16:39 | comment | added | PSHINH2 | @SamHopkins Thanks for your help! Would you also possibly know how to find the most negative root for a given basis? | |
| Jun 16, 2022 at 16:37 | comment | added | Sam Hopkins | Yes, that is what I meant. I am not sure if there is a more efficient way. Probably this particular computation has been done before, though. | |
| Jun 16, 2022 at 16:29 | comment | added | PSHINH2 | @SamHopkins I assume this is the algorithm where you take one of the connected components of your Dynkin diagram extend by the most negative root and delete some subset of vertices of this component? It seems like quite a lengthy calculation and it seems to give a lot of subroot systems of the same type which I am not sure how to check are Weyl equivalent. | |
| Jun 16, 2022 at 16:03 | comment | added | Sam Hopkins | You can use Borel-de Siebenthal theory to find the maximal subroot systems, then induct. I guess at some point you also have to consider maximal parabolic subroot systems as well. | |
| S Jun 16, 2022 at 16:01 | review | First questions | |||
| Jun 16, 2022 at 17:08 | |||||
| S Jun 16, 2022 at 16:01 | history | asked | PSHINH2 | CC BY-SA 4.0 |