English

Hyperbolic reflection groups associated to the quadratic forms $-3x_0^2 + x_1^2 + ... + x_n^2$

Group Theory 2010-09-29 v3

Abstract

We determine the maximal hyperbolic reflection groups associated to the quadratic forms 3x02+x12+...+xn2-3x_0^2 + x_1^2 + ... + x_n^2, n2n \ge 2, and present the Coxeter schemes of their fundamental polyhedra. These groups exist in dimensions up to 13, and a proof is given that in higher dimensions these quadratic forms are not reflective.

Keywords

Cite

@article{arxiv.1007.2299,
  title  = {Hyperbolic reflection groups associated to the quadratic forms $-3x_0^2 + x_1^2 + ... + x_n^2$},
  author = {John Mcleod},
  journal= {arXiv preprint arXiv:1007.2299},
  year   = {2010}
}

Comments

16 pages, 7 figures

R2 v1 2026-06-21T15:47:56.857Z