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ON PAIRED ROOT SYSTEMS OF COXETER GROUPS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  18 June 2018

XIANG FU
XIANG FU*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing, China email fuxiang@math.pku.edu.cn
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Abstract

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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.

Keywords

Coxeter groupsKac–Moody Lie algebrasroot systemsTits cone

MSC classification

Primary: 20F55: Reflection and Coxeter groups
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata 20F65: Geometric group theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 105 , Issue 3 , December 2018 , pp. 347 - 365
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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