Timeline for How big can the index inside the root lattice of the lattice generated by a subset of roots be?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 20, 2018 at 20:00 | vote | accept | Sam Hopkins | ||
| Sep 20, 2018 at 19:54 | answer | added | LSpice | timeline score: 4 | |
| Sep 19, 2018 at 14:01 | history | edited | Sam Hopkins | CC BY-SA 4.0 |
added 13 characters in body
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| Sep 18, 2018 at 21:58 | comment | added | LSpice | In particular, I think that Borel–de Siebenthal theory should enumerate the possibilities, and you can just check the indices in the various cases. | |
| Sep 18, 2018 at 21:57 | comment | added | LSpice | Let $G$ be the adjoint group of type $\Phi$, and $H$ the subgroup of $G$ generated by the roots in $S$. Then your index is the size of the centre of $H$. (This is true over, say, an algebraically closed field of characteristic $0$. I don't know how to make sense of it over the integers, but I also don't know that it can't be made sense of in that setting.) | |
| Sep 18, 2018 at 21:34 | history | asked | Sam Hopkins | CC BY-SA 4.0 |