Timeline for Is $Spin(N)$ a subgroup of $SU(N)$
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2021 at 18:31 | comment | added | Марина Marina S | (2) Please see a related post of mine math.stackexchange.com/q/4216056/955245 --- Relation between the ππ(8), π(8), and ππππ(8) | |
| Aug 20, 2021 at 18:30 | comment | added | Марина Marina S | dear all of you, (1) can you also confirm whether $π(8) \supset ππππ(8)$ or π(8)β ππππ(8) ? thanks! | |
| Aug 4, 2021 at 2:07 | comment | added | David E Speyer | @anniemariecΕur Yes -- except that I didn't do the check mentioned in the conversation with LSpice above. | |
| Aug 3, 2021 at 18:50 | comment | added | annie marie cœur | Am I correct to summarize your answer that Spin(N) $\subset SU(N)$ for $N \leq 6$, but Spin(N) $\not \subset SU(N)$ for $N \geq 7$? thanks! (voted +1) | |
| Mar 21, 2018 at 17:06 | comment | added | David E Speyer | The way I'd give a careful proof is to look at the Weyl Dimension Formula and check that the only representations of $\mathrm{Spin}(8)$ of dimension $\leq 8$ are the trivial rep and the three representations related by triality. I will admit I haven't done this, although I don't think it will be hard. | |
| Mar 21, 2018 at 16:54 | comment | added | LSpice | This is a great answer! Is it obvious that, because the natural $8$-dimensional unitary representations of $\mathrm{Spin}(8)$ have kernel, there is no faithful $8$-dimensional unitary representation of $\mathrm{SU}(8)$? | |
| Mar 21, 2018 at 13:12 | history | edited | David E Speyer | CC BY-SA 3.0 |
added 76 characters in body
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| Mar 21, 2018 at 11:31 | history | answered | David E Speyer | CC BY-SA 3.0 |