Timeline for Weyl groups of $E_6$ and $E_7$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2014 at 21:52 | comment | added | Noam D. Elkies | You're welcome. The ATLAS has references in the back, sorted by group, which should help get you started. Meanwhile I should have written ${\rm O}^-_6$, not just ${\rm O}_6$, because in even dimension there are two inequivalent quadratic forms (and ${\rm Sp}_6(2)$ contains both of the groups ${\rm O}^\pm_6(2)$). | |
| Dec 26, 2014 at 20:21 | answer | added | Jim Humphreys | timeline score: 7 | |
| Dec 26, 2014 at 19:48 | comment | added | Hebe | I see. Thank you. Is there any reference book or paper which gives the concrete description for the simple reflections in the symplectic group? | |
| Dec 26, 2014 at 19:28 | comment | added | Noam D. Elkies | Over the field of $2$ elements. | |
| Dec 26, 2014 at 19:22 | comment | added | Hebe | Thank you for your comment, professor Elkies. What is $Sp_6(2)$? Is it the 6 by 6 symplectic group over a finite field of characteristic 2? | |
| Dec 26, 2014 at 19:06 | comment | added | Noam D. Elkies | The 6-dimensional spaces being $E_6/2E_6$ and $E_7/2E_7^*$ (where $E_6$, $E_7$ are the respective root lattices). It must be possible to find this in the ATLAS pages for those two groups. | |
| Dec 26, 2014 at 19:03 | comment | added | Noam D. Elkies | How do you understand these simple groups? The $E_7$ one is ${\rm Sp}_6(2)$; in general ${\rm Sp}_{2n}$ contains ${\rm O}_{2n}$ in characteristic $2$, and indeed ${\rm O}_6(2)$ is one description of the $E_6$ group. | |
| Dec 26, 2014 at 18:48 | history | asked | Hebe | CC BY-SA 3.0 |