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

John Mcleod

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arXiv · 1007.2299

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

John Mcleod

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Abstract

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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BibTeX RIS

John Mcleod. 2010-09-28. Hyperbolic reflection groups associated to the quadratic forms $-3x_0^2 + x_1^2 + ... + x_n^2$. https://arxiv.org/abs/1007.2299

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