Timeline for Is there any Lefschetz-like principle for representations of finite groups?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 3, 2015 at 4:25 | comment | added | Geoff Robinson | I have given a characteristic 0 example. In characteristic 3, the simple group PSU(3,3) has an absolutely irreducible representation of degree 15, but has order 6048. There are many more examples in the "Atlas of Brauer Characters". | |
| Feb 3, 2015 at 2:38 | comment | added | P Vanchinathan | @Geoff Robinson: Thanks for your valuable comment connecting Eisenstein criterion. Learnt something new. I am curious about irreducible degrees not dividing the order of the group. Surprised that such a fact is not mentioned in textbooks. Can you direct me to a reference for an example of that? | |
| Feb 2, 2015 at 17:16 | comment | added | Jay Taylor | That's a nice example for $C_p$, I'd never thought about that before. | |
| Feb 2, 2015 at 17:11 | comment | added | Geoff Robinson | To supplement this: note by the way that when $p$ is odd, Eisenstein's criterion tells us that the cyclic group of order $p$ has an irreducible representation of degree $p-1$ over $\mathbb{Q}$, so the degree of an irreducible characteristic $0$ representation need not divide the group order in general. Also, the degrees of irreducible characteristic $p$ representations (even over algebraically closed fields) need not divide the group order. | |
| Feb 2, 2015 at 16:57 | vote | accept | P Vanchinathan | ||
| Feb 2, 2015 at 16:55 | history | answered | Jay Taylor | CC BY-SA 3.0 |