English

The Unknown Subgroup of $Aut(E_8)$

Group Theory 2018-02-16 v2

Abstract

The E8E_8 lattice has been thoroughly studied for more than a century and nearly all the maximal subgroups of W(E8)W(E_8) have been described-all except 2A92A_9. We will show that 2A92A_9 has simple descriptions from three different perspectives: looking at E8/2E8E_8/2E_8; looking at the lattice's norm 2 vectors; and looking at its norm 4 vectors. Two of the three descriptions are especially simple: 2A92A_9 stabilizes a partition of the 2160 norm 4 vectors into nine scale copies of E8E_8; and 2A92A_9 stabilizes a partition of the 135 isotropic points of E8/2E8E_8/2E_8 into nine disjoint isotropic 4-spaces of 15 points each (so the well-known known isomorphism A8A_8 \cong L4L_4(2) is visible within E8E_8.)

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

R2 v1 2026-06-22T21:45:25.517Z