The Unknown Subgroup of $Aut(E_8)$
Group Theory
2018-02-16 v2
Abstract
The lattice has been thoroughly studied for more than a century and nearly all the maximal subgroups of have been described-all except . We will show that has simple descriptions from three different perspectives: looking at ; looking at the lattice's norm 2 vectors; and looking at its norm 4 vectors. Two of the three descriptions are especially simple: stabilizes a partition of the 2160 norm 4 vectors into nine scale copies of ; and stabilizes a partition of the 135 isotropic points of into nine disjoint isotropic 4-spaces of 15 points each (so the well-known known isomorphism (2) is visible within .)
Keywords
Cite
@article{arxiv.1709.05532,
title = {The Unknown Subgroup of $Aut(E_8)$},
author = {Majid Butler and De'janeke Johnson and Tomme Denney and Sandernisha Claiborne and Tianna Robinson},
journal= {arXiv preprint arXiv:1709.05532},
year = {2018}
}
Comments
3 pages. The 9*240 norm 4 vectors form 9 scale copies of E8