Timeline for Sporadic subgroup of E7
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 29, 2019 at 10:25 | comment | added | YCor | What is "the Lie group of type E7"? the complex one? the compact one? the split real one? (for embedding finite subgroups the first two are equivalent and I guess this is the intended meaning) | |
| Aug 29, 2019 at 1:27 | answer | added | Theo Johnson-Freyd | timeline score: 8 | |
| Jul 20, 2019 at 16:02 | comment | added | Theo Johnson-Freyd | @DavidTreumann You really should post that as an answer! | |
| Jun 9, 2018 at 20:48 | comment | added | David Treumann | The finite simple groups (and their central extensions) that embed into exceptional Lie groups were classified across many papers. There is a summary by Griess and Ryba here. J1 does not appear to be one of them. But incidentally following Victor's suggestion I got Sym^4(56)^{J1} is 8-dimensional, for both the 56-dimensional representations. | |
| Jun 6, 2018 at 20:05 | comment | added | Victor Petrov | Another obvious check: if J1 embeds into E7, the 56-dimensional representation must carry invariant 4-form, so the fourth symmetric power must contain a trivial representation. I guess it can be checked via the character table and, if not, the conjecture is false, and if yes, you can try to catch this 4-form and compare it to that for E7. | |
| Jun 2, 2018 at 21:22 | comment | added | Noam D. Elkies | J1 is a subgroup of a reduction of G2 mod 11. Possibly one can find a copy of G2 in E7 and show that the resulting linear representations mod 11 lift to characteristic zero. (This guess is motivated by the known observation that Thompson's sporadic group, though not contained in E8(C), is a subgroup of a reduction mod 3 of E8 and has a 248-dimensional representation over C.) | |
| Jun 2, 2018 at 20:35 | comment | added | Ievgen Makedonskyi | For the dimension of next smalles representation we have: 912=209+3*133+4*76. | |
| Jun 2, 2018 at 20:18 | comment | added | André Henriques | If there is an embedding J1 --> E7, then the next smallest representations of E7 should also decompose into (hopefully few) J1-representations. Have you checked whether that is indeed the case? | |
| Jun 2, 2018 at 19:54 | review | First posts | |||
| Jun 2, 2018 at 22:47 | |||||
| Jun 2, 2018 at 19:49 | history | asked | Ievgen Makedonskyi | CC BY-SA 4.0 |