Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

Vadim Bugaenko, Yonah Cherniavsky, Tatiana Nagnibeda, Robert Shwartz

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)17-27
Number of pages11
JournalDiscrete Applied Mathematics
Volume192
DOIs
StatePublished - 10 Sep 2015

Keywords

  • Balanced functions on graphs
  • Coxeter graphs
  • Coxeter groups
  • Geometric representation
  • Numbers game
  • Signed graphs
  • Weighted graphs

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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