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Nov 22, 2017 at 15:38 comment added Jay Taylor If you want to see how difficult this problem can be check out Geoff Robinsons DPhil Thesis. There he classifies the irreducible subgroups of $\mathrm{GL}_{11}(\mathbb{C})$. It's quite the feat considering it's pre-classification of finite simple groups. homepages.abdn.ac.uk/d.j.benson/papers/r/robinson/thesis.dvi
Nov 22, 2017 at 10:45 history edited Sebastien Palcoux
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Nov 22, 2017 at 2:33 answer added Sebastien Palcoux timeline score: 4
Nov 22, 2017 at 1:12 comment added Qiaochu Yuan Noah means faithful irrep, although this condition is automatic if $G$ is simple.
Nov 22, 2017 at 0:39 comment added Noah Snyder For $GL_n$ you're just asking about groups with an $n$-dimensional irrep, for $O_n$ and $SP_n$ you're asking for an $n$-dimensional irrep with FS-indicator $\pm 1$ (respectively). That's clearly too broad a question to hope to say much. You might be interested in Jordan's Theorem or this paper.
Nov 22, 2017 at 0:22 history asked Shawn CC BY-SA 3.0