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ON PAIRED ROOT SYSTEMS OF COXETER GROUPS

Published online by Cambridge University Press:  18 June 2018

XIANG FU*
Affiliation:
Beijing International Center for Mathematical Research, Peking University, Beijing, China email [email protected]
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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.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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