ON PAIRED ROOT SYSTEMS OF COXETER GROUPS

被引：3

作者：

Fu, Xiang ^{[1
]}

机构：

[1] Peking Univ, Beijing Int Ctr Math Res, Beijing, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2018年 / 105卷 / 03期

关键词：

Coxeter groups; Kac-Moody Lie algebras; Tits cone; root systems;

D O I：

10.1017/S1446788717000350

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper examines a systematic method of constructing a pair of (inter-related) root systems for arbitrary Coxeter groups from a class of nonstandard geometric representations. This method can be employed to construct generalizations of root systems for a large family of linear groups generated by involutions. We then give a characterization of Coxeter groups, among these groups, in terms of such paired root systems. Furthermore, we use this method to construct and study the paired root systems for reflection subgroups of Coxeter groups.

引用

页码：347 / 365

页数：19

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