Timeline for Is one of the hyperplane partitions of a irreducible root system always generate the whole Weyl group?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 6, 2019 at 10:55 | comment | added | Christoph Mark | You are right. I got it wrong. | |
| Oct 6, 2019 at 9:26 | comment | added | Zhaoting Wei | @user66288 This is not trivially true. Actually let $\Phi^+$ and $\Psi^+$ be too positive root systems. My question is equivalent to the question whether one of $\Phi^+\cap \Psi^+$ and $\Phi^+\cap \Psi^-$ generates the whole Weyl group. | |
| Oct 6, 2019 at 4:55 | comment | added | Christoph Mark | I have the impression this is trivially true. Changing the hyperplane corresponds to a different choice of positive roots. So, your example already covers this. | |
| Oct 2, 2019 at 22:57 | comment | added | Sam Hopkins | I feel like there should be a way to reduce this to considering $2$-dimensional subspaces... | |
| Oct 2, 2019 at 19:49 | history | asked | Zhaoting Wei | CC BY-SA 4.0 |