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

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

2010-07-14

arxiv.org/abs/1007.2299v3

Mathematics

Group Theory

16 pages, 7 figures

Scientific paper

We determine the maximal hyperbolic reflection groups associated to the
quadratic forms $-3x_0^2 + x_1^2 + ... + x_n^2$, $n \ge 2$, 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.

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