Normalizers of Parabolic Subgroups of Coxeter Groups
Group Theory
2014-10-01 v1
Abstract
We improve a bound of Borcherds on the virtual cohomological dimension of the non-reflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink's result that the non-reflection part of a reflection centralizer is free. Namely, the non-reflection part of the normalizer of parabolic subgroup of type D5 or Aodd is either free or has a free subgroup of index 2.
Keywords
Cite
@article{arxiv.1105.0253,
title = {Normalizers of Parabolic Subgroups of Coxeter Groups},
author = {Daniel Allcock},
journal= {arXiv preprint arXiv:1105.0253},
year = {2014}
}
Comments
7 pages