Timeline for A small rank linear combination of a small number of elements of a group
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9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 1, 2015 at 10:34 | vote | accept | Mikhail Borovoi | ||
| Dec 30, 2014 at 16:10 | answer | added | Andreas Thom | timeline score: 3 | |
| Dec 30, 2014 at 12:23 | comment | added | Klim Efremenko | @Geoff Robinson: for the natural irreducible representation of degree $n−1$ of the symmetric group $S_n$ it is easy to see that: $m(2,G,\rho)=1$. To see it take $id-(1,2)$, where $(1,2)$ permutation of $1$ and $2$. The only problem with this example is that $\log|G|>dim \rho$. | |
| Dec 30, 2014 at 12:19 | comment | added | Klim Efremenko | @Andreas Thom : Can you prove it? I would like to see the proof. | |
| Dec 30, 2014 at 11:57 | comment | added | Lior Bary-Soroker | @StefanKohl This question arises in the work of Klim Efremenko on locally decodable codes, see his paper ocf.berkeley.edu/~klimefre/papers/Induced.pdf | |
| Dec 29, 2014 at 18:59 | comment | added | Geoff Robinson | I think this may be tricky for the natural irreducible representation of degree $n-1$ of the symmetric group $S_{n}$, though I can't give precise statements. | |
| Dec 29, 2014 at 17:02 | comment | added | Stefan Kohl♦ | In which context does this question arise, i.e. is there a particular reason why you are interested in properties of sums or linear combinations of values of a representation? -- Unless you know a particular reason why this is not so, it seems conceivable that these matrices are additively more-or-less unrelated, and that your question is thus very hard, but not very interesting. | |
| Dec 29, 2014 at 12:21 | history | asked | Mikhail Borovoi | CC BY-SA 3.0 |