English

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.

Keywords

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

R2 v1 2026-06-21T23:52:21.471Z