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Dec 13, 2019 at 0:04 comment added Will Jagy @NoamD.Elkies this question seems your sort of thing, from yesterday: mathoverflow.net/questions/348159/…
Dec 11, 2019 at 23:49 vote accept LeechLattice
Dec 11, 2019 at 10:15 answer added Nick Gill timeline score: 14
Dec 11, 2019 at 5:35 comment added abx You forgot $A_8=GL(4,2)$ (which has a nice and simple geometric interpretation).
Dec 11, 2019 at 4:17 comment added Noam D. Elkies What's "finite geometry"?$$ $$ This group appears in three complex reflection groups; one is the Weyl group of $E_6$, whose reductions mod $2$ and $3$ identify it with $O_6^-(2)$ and $O_5(3)$; another is the complex (Eisenstein) $E_8$ lattice, whose reductions mod $2$ and $3$ take us to the same groups in their $U_4$ and $Sp_4$ guises which you asked about. Short vectors in each lattice give rise to several geometrical structures on which the group acts, including the $27$ lines of a cubic surface and the $36$ pairs $\pm r$ of $E_6$ roots.
Dec 11, 2019 at 2:03 history edited LeechLattice CC BY-SA 4.0
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Dec 11, 2019 at 1:42 history asked LeechLattice CC BY-SA 4.0