Weighted Coxeter graphs and generalized geometric representations of Coxeter groups

被引：8

作者：

Bugaenko, Vadim ^{[1
]}

Cherniavsky, Yonah ^{[1
]}

Nagnibeda, Tatiana ^{[2
]}

Shwartz, Robert ^{[1
]}

机构：

[1] Ariel Univ, Dept Math & Comp Sci, Ariel, Israel

[2] Univ Geneva, Dept Math, CH-1211 Geneva 4, Switzerland

来源：

DISCRETE APPLIED MATHEMATICS | 2015年 / 192卷

基金：

瑞士国家科学基金会;

关键词：

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

D O I：

10.1016/j.dam.2014.05.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：17 / 27

页数：11

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