Timeline for The finite subgroups of SU(n)
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 11, 2022 at 0:00 | comment | added | Ian Gershon Teixeira | That was really helpful! I used it to write up math.stackexchange.com/questions/4539427/… . I'm not expecting an answer to this but if you know any references for finite subgroups of $ SO_7(\mathbb{R}) $ I would be very interested to see them! | |
| Sep 27, 2022 at 9:06 | comment | added | José Figueroa-O'Farrill | @IanGershonTeixeira Not sure right now. However, since the universal cover of $SO_5(\mathbb{R})$ is $\operatorname{Spin}(5) \cong \operatorname{Sp}(2)$, you may be able to look for finite subgroups of $2 \times 2$ quaternionic matrices. A quick google came up with this: core.ac.uk/download/pdf/82740228.pdf | |
| Sep 26, 2022 at 17:08 | comment | added | Ian Gershon Teixeira | Thanks for the code it was very interesting! Recently I've been interested in finite subgroups of $ SO_5(\mathbb{R}) $. Would you happen to know any references that discuss the finite subgroups of $ SO_5(\mathbb{R}) $? For example you mentioned that an algorithm of Zassenhaus has been used on $ SO_n $ for at least $ n=6 $. | |
| Jun 3, 2022 at 8:05 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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| Mar 2, 2022 at 8:37 | comment | added | José Figueroa-O'Farrill | @IanGershonTeixeira I'm afraid it's not particularly well documented, but here it is: dropbox.com/s/63drrattjugkzo7/SU3subgroupOrder360Again.nb?dl=0 | |
| Apr 2, 2010 at 19:47 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
added 345 characters in body
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| Apr 2, 2010 at 14:23 | comment | added | José Figueroa-O'Farrill | Indeed -- I just had Mathematica check the order of the group generated by the explicit SU(3) matrices in the paper of Fairbairn et al. and it has order 1080. | |
| Apr 2, 2010 at 6:07 | comment | added | Dylan Thurston | Reading a little more closely, it seems that the group with the 3-dimensional representation is not $A_6$, but rather a $\mathbb{Z}/3$ central extension of $A_6$. | |
| Apr 2, 2010 at 0:44 | comment | added | José Figueroa-O'Farrill | Apparently it is sci.math, not sci.math.research -- sorry. How I wish I could edit comments! | |
| Apr 2, 2010 at 0:44 | comment | added | José Figueroa-O'Farrill | I forgot to link to the sci.math.research thread. Here it is: sci.tech-archive.net/Archive/sci.math/2005-03/5511.html | |
| Apr 1, 2010 at 22:32 | comment | added | José Figueroa-O'Farrill | In fact, this statement already appears in the book of Blichfeldt, Dickson and Miller which Bruce Westbury mentions in his answer. It is claimed that this group is simple. There is a thread in sci.math.research claiming that any simple group of order 360 is isomorphic to $A_6$. If so, then the mistake is in claiming that the group is simple, because as you point out, $A_6$ has no nontrivial representation of dimension 3. (The smallest is of dimension 5.) I must admit that I have not gone through their proof, so cannot say where the error lies. | |
| Apr 1, 2010 at 6:24 | comment | added | Dylan Thurston | The Fairbairn, Fulton and Klink paper has at least one error: they claim that $A_6$ appears as a finite subgroup of $\mathrm{SU}(3)$, but $A_6$ has no 3-dimensional representations, as indeed their character table shows. What is the group of order 360 that appears? | |
| Mar 18, 2010 at 16:22 | vote | accept | Q.Q.J. | ||
| Mar 4, 2010 at 13:30 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
Added some links
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| Mar 4, 2010 at 11:51 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
added 243 characters in body
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| Mar 4, 2010 at 11:44 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |