Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

Vadim Bugaenko; Yonah Cherniavsky; Tatiana Nagnibeda; Robert Shwartz

doi:10.1016/j.dam.2014.05.012

Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

Vadim Bugaenko, Yonah Cherniavsky, Tatiana Nagnibeda, Robert Shwartz

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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 language	English
Pages (from-to)	17-27
Number of pages	11
Journal	Discrete Applied Mathematics
Volume	192
DOIs	https://doi.org/10.1016/j.dam.2014.05.012
State	Published - 10 Sep 2015

Keywords

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

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10.1016/j.dam.2014.05.012

Cite this

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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.",

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AB - 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.

KW - Balanced functions on graphs

KW - Coxeter graphs

KW - Coxeter groups

KW - Geometric representation

KW - Numbers game

KW - Signed graphs

KW - Weighted graphs

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Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

Abstract

Keywords

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