Timeline for How to construct groups and large dimension representations? How about faithful ones?
Current License: CC BY-SA 4.0
12 events
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| Feb 13, 2019 at 13:35 | comment | added | Geoff Robinson | @JeremyRickard : I don't think you said quite what you meant. I think it is true that for every integer $n$ there is finite group $G$ with a faithful complex irreducible character of degree $n$ and with $n = \sqrt{[G:Z(G)]}.$ | |
| Feb 13, 2019 at 9:50 | comment | added | user135743 | @JeremyRickard Sorry for the unclear statement, I meant that for a fixed $D$, for large $G$, with say trivial center, then $dim(V)^2<=G - D$ | |
| Feb 13, 2019 at 9:48 | vote | accept | user135743 | ||
| Feb 13, 2019 at 8:14 | comment | added | Jeremy Rickard | I don't understand the sentence starting "One cannot hope ...". It's not clear to me exactly what you want to bound in terms of what. Obviously, for every $n>0$ there is a group $G$ with $|G|=n$ and an irreducible representation of degree exactly $\sqrt{|G:Z(G)|}$ ... and often there's even a nonabelian one. Such groups are called "of central type", by the way. | |
| Feb 13, 2019 at 0:33 | answer | added | Alex B. | timeline score: 9 | |
| Feb 12, 2019 at 22:52 | comment | added | YCor | Yep, well it's easy only when you take the number of conjugacy classes as granted. | |
| Feb 12, 2019 at 22:41 | comment | added | user135743 | @YCor That is correct. I edited it, just meant an average argument | |
| Feb 12, 2019 at 22:40 | history | edited | user135743 | CC BY-SA 4.0 |
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| Feb 12, 2019 at 22:00 | comment | added | YCor | Just to be sure, you want estimates on $c(G)=$ sup of dimension of irreducibles of $G$, right? I don't really understand about all this stuff about small number of conjugacy classes: if it's an "easy" lower bound you should be able to give it explicitly. | |
| Feb 12, 2019 at 21:56 | history | edited | YCor |
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| Feb 12, 2019 at 21:50 | review | First posts | |||
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| Feb 12, 2019 at 21:49 | history | asked | user135743 | CC BY-SA 4.0 |