Timeline for Relation between positive roots of $E_8$ and $\mathbb{F}_2^8 \setminus \{0\}$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 11, 2023 at 16:54 | history | edited | LSpice | CC BY-SA 4.0 |
TeX, while this is on the front page
|
| Aug 13, 2022 at 20:46 | vote | accept | IMeasy | ||
| Aug 13, 2022 at 16:04 | comment | added | IMeasy | I have edited the question to make a better link with the answers. | |
| Aug 13, 2022 at 16:02 | history | edited | IMeasy | CC BY-SA 4.0 |
deleted 33 characters in body; edited title
|
| Aug 13, 2022 at 0:08 | answer | added | Theo Johnson-Freyd | timeline score: 8 | |
| Aug 12, 2022 at 17:27 | comment | added | Sam Hopkins | A construction of the E8 root system is described here: en.wikipedia.org/wiki/E8_(mathematics)#E8_root_system | |
| Aug 12, 2022 at 14:21 | comment | added | abx | The positive roots correspond to vectors with $q=1$ for the induced quadratic form. This is described for instance in Exercise 1 of Bourbaki Lie groups and Lie algebras, ch. VI, §4. | |
| Aug 12, 2022 at 14:07 | comment | added | IMeasy | Yes, you are right, I am quite confused. The reduction modulo 2 of $E_8$ must have a quadratic form with values in $\mathbb{F}_2$ hence there is a non trivial map from $W(E_8)$ to the orthogonal group $O^+(8,\mathbb{F}_2)$ (with kernel $\pm 1$). So what is the relation with $\mathbb{F}_2^8$? | |
| Aug 12, 2022 at 13:55 | comment | added | abx | I don't understand: $E_8$ has 120 positive roots, but $2^8-1=255$. | |
| Aug 12, 2022 at 13:42 | history | asked | IMeasy | CC BY-SA 4.0 |