Timeline for The lower bound of a group with characters of special degrees
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 1, 2015 at 3:19 | comment | added | Qiaochu Yuan | Related: mathoverflow.net/questions/530/… | |
| May 31, 2015 at 19:54 | vote | accept | BHZ | ||
| May 31, 2015 at 13:07 | answer | added | Geoff Robinson | timeline score: 8 | |
| May 31, 2015 at 10:32 | history | edited | Derek Holt |
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| May 31, 2015 at 9:00 | comment | added | BHZ | Thanks for the comments and hints. I asked the above question for the complex irreducible characters. | |
| May 31, 2015 at 8:53 | comment | added | Duchamp Gérard H. E. | @GeoffRobinson Ok for the terminology. A Jordan block of size greater than one never acts irreducibly (in particular, as you noted, in characteristic $p$). Can the OP make precise whether it is real, complex or any characteristic ? | |
| May 31, 2015 at 8:43 | comment | added | Geoff Robinson | @DuchampGérardH.E.: I interpreted this as a question about complex irreducible characters. Even in characteristic $p$, a Jordan block of size greater than $1$ does not act irreducibly (it does act indecomposably). | |
| May 31, 2015 at 8:33 | comment | added | Duchamp Gérard H. E. | For $p$, I think it's $p$ itself as, if you denote $l(p)$ this lower bound, one must have $p\leq l(p)$ (because of the regular representation) and, contrariwise, $l(p)\leq p$ because of the existence of the group in $Gl(p)$ generated by a maximal Jordan block with $1$ as eigenvalue. For $p^k, k\geq 2$, I do not know. | |
| May 31, 2015 at 8:30 | comment | added | Geoff Robinson | In the case $p$, the lowest possible order, given the orthogonality relations would be $p^{2}+p$. This order can be attained, but only when $p=2$ or $p$ is a Mersenne prime, in which case there is a Frobenius group of order $p(p+1)$ with kernel of order $p+1$ and complement of order $p$. | |
| May 31, 2015 at 8:22 | history | edited | BHZ | CC BY-SA 3.0 |
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| May 31, 2015 at 8:09 | history | asked | BHZ | CC BY-SA 3.0 |