Timeline for Which groups have only real and quaternionic irreducible representations?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2010 at 16:37 | answer | added | Faisal | timeline score: 4 | |
| Nov 27, 2010 at 16:35 | answer | added | Skip | timeline score: 6 | |
| Nov 27, 2010 at 16:24 | vote | accept | John Baez | ||
| Nov 27, 2010 at 16:24 | comment | added | John Baez | @Kevin: Yes, that's what I'm asking for. I'd known all irreps of symmetric groups were defined over the rationals but somehow hadn't applied that knowledge to this puzzle (I think this is known as "stupidity"). Torsten's answer hits the nail on the head and I'm actually pleased to know there are so many examples. | |
| Nov 27, 2010 at 12:28 | comment | added | Kevin Buzzard | @John: for finite groups, aren't you just asking for examples where the character table is real?? This is not at all uncommon. Dihedral group order 8, quaternion group order 8, all symmetric groups, product of groups for which the character table is real... | |
| Nov 27, 2010 at 11:34 | answer | added | Torsten Ekedahl | timeline score: 34 | |
| Nov 27, 2010 at 9:28 | comment | added | Alex B. | See also this question, which is concerned with finite groups: mathoverflow.net/questions/42646/… | |
| Nov 27, 2010 at 9:23 | comment | added | Angelo | I don't know the answer, but among finite groups there are many cases in which this happens. For example, every representation of a finite symmetric group is defined over the rationals, so in particular it is real. | |
| Nov 27, 2010 at 9:06 | history | edited | John Baez | CC BY-SA 2.5 |
added 44 characters in body
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| Nov 27, 2010 at 8:55 | history | asked | John Baez | CC BY-SA 2.5 |