Timeline for Type of 26-dimensional representation of different real forms of the complex simple Lie algebra $F_4$
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| May 9, 2012 at 17:03 | answer | added | Vít Tuček | timeline score: 4 | |
| May 4, 2012 at 20:05 | vote | accept | José Figueroa-O'Farrill | ||
| May 4, 2012 at 18:50 | answer | added | Marty | timeline score: 12 | |
| May 4, 2012 at 17:04 | comment | added | José Figueroa-O'Farrill | Not really. The maximal compact of $F_4^{-20}$ is $\operatorname{Spin}(9)$, under which the 26-dimensional representation breaks up as a direct sum of the trivial 1-dimensional rep, the defining 9-dimensional rep and the 16-dimensional spinor rep. That reducible $\Spin(9)$-module admits invariant inner products of signatures $(25,1)$ and $(16,10)$, among others. | |
| May 4, 2012 at 16:32 | comment | added | Bruce Westbury | Can you settle the case $F_4^{-20}$ by restricting the 26 dimensional representation to the maximal compact subgroup? | |
| May 4, 2012 at 16:23 | history | edited | José Figueroa-O'Farrill | CC BY-SA 3.0 |
added some more details of my confusion
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| May 4, 2012 at 15:28 | answer | added | Bruce Westbury | timeline score: 1 | |
| May 4, 2012 at 14:42 | answer | added | Jim Humphreys | timeline score: 4 | |
| May 4, 2012 at 13:56 | history | edited | José Figueroa-O'Farrill | CC BY-SA 3.0 |
Followed Theo's suggestion and changed \mathrm to \operatorname.
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| May 4, 2012 at 13:27 | comment | added | Theo Johnson-Freyd |
(TeXnical comment: use \operatorname rather than \mathrm in $\kappa(X,Y) = \dots$ to make the spacing work; currently "tr ad" runs together into "trad".) Nice question.
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| May 4, 2012 at 12:51 | history | asked | José Figueroa-O'Farrill | CC BY-SA 3.0 |