The reflective Lorentzian lattices of rank 3

Details The reflective Lorentzian lattices of rank 3 The reflective Lorentzian lattices of rank 3

2010-10-04

arxiv.org/abs/1010.0486v2

Mathematics

Group Theory

Revision includes much more explicit information in the table, and some other improvements. The TeX file is also a Perl script

Scientific paper

We classify all the symmetric integer bilinear forms of signature (2,1) whose isometry groups are generated up to finite index by reflections. There are 8595 of them up to scale, whose 374 distinct Weyl groups fall into 39 commensurability classes. This extends Nikulin's enumeration of the strongly square-free cases. Our technique is an analysis of the shape of the Weyl chamber, followed by computer work using Vinberg's algorithm and our "method of bijections". We also correct a minor error in Conway and Sloane's definition of their canonical 2-adic symbol.

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