A characterization of finitely generated reflection subgroups of Coxeter groups orthogonal to a reflection
Group Theory
2012-01-18 v2
Abstract
Given a reflection in a Coxeter group (possibly of infinite rank), we consider the subgroup of generated by the reflections in having (-1)-eigenvectors orthogonal to the (-1)-eigenvector of . In this paper, we determine completely when this subgroup is finitely generated, by using preceding results on centralizers of reflections. This result provides a new and naturally constructed example of a family of non-finitely generated subgroups of finitely generated groups.
Keywords
Cite
@article{arxiv.math/0603667,
title = {A characterization of finitely generated reflection subgroups of Coxeter groups orthogonal to a reflection},
author = {Koji Nuida},
journal= {arXiv preprint arXiv:math/0603667},
year = {2012}
}
Comments
21 pages; previously entitled "On reflections in Coxeter groups commuting with a reflection" (v2) presentation improved