Timeline for Failure of a basic fact from Representation Theory
Current License: CC BY-SA 3.0
12 events
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
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| May 7, 2013 at 2:43 | comment | added | Qiaochu Yuan | @Yemon: yes, and I don't remember. I think parts of the argument come up in the McKay correspondence. | |
| May 7, 2013 at 0:19 | comment | added | Yemon Choi | Also, Qiaochu, do you know of a reference for the argument you give, or was it just something that emerged when you were learning representation theory? For a short note I'm typing up, I would like to both cite the result and indicate (since the note will probably be read by functional/harmonic analysts) that the proof doesn't require Feit-Thompson. | |
| May 7, 2013 at 0:17 | comment | added | Yemon Choi | I am probably the only person who got confused, but just in case anyone else was also wondering: am I right in saying that the argument avoids Feit-Thompson by saying "assume G has an irrep of degree 2, then G must have even order, then G must have an involution," etc? | |
| Aug 7, 2012 at 19:31 | comment | added | Qiaochu Yuan | @Mariano: well, in characteristic $0$ over a splitting field it only depends on the first step... | |
| Aug 7, 2012 at 17:05 | comment | added | Mariano Suárez-Álvarez | In the second step of tour proof you mention Cauchy's theorem but that depends on the Feit-Thompson theorem, which is a few hundred orders of magnitude more complex... :-) | |
| Aug 7, 2012 at 1:15 | comment | added | Qiaochu Yuan | @Geoff: thanks for the comment. The proof I'm familiar with fails but I didn't know if a different technique could work in positive characteristic. | |
| Aug 7, 2012 at 0:40 | comment | added | Geoff Robinson | The first step does not usually work in prime characteristic, but does work for solvable groups by the fairly difficult Fong-Swan theorem. | |
| Aug 7, 2012 at 0:03 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 6, 2012 at 23:58 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 6, 2012 at 23:50 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Aug 6, 2012 at 23:35 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |