Weighted Coxeter graphs and generalized geometric representations of Coxeter Groups
Combinatorics
2014-05-07 v3
Abstract
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a representation. In the case when the weighted Coxeter graph is balanced we discuss how the generalized geometric representation is related to the numbers game played on the Coxeter graph.
Cite
@article{arxiv.1304.0692,
title = {Weighted Coxeter graphs and generalized geometric representations of Coxeter Groups},
author = {Vadim Bugaenko and Yonah Cherniavsky and Tatiana Nagnibeda and Robert Shwartz},
journal= {arXiv preprint arXiv:1304.0692},
year = {2014}
}
Comments
accepted to Discrete Applied Mathematics