Maximal order Abelian subgroups of Coxeter groups

John M. Burns; Goetz Pfeiffer

doi:10.1017/S0017089522000143

Maximal order Abelian subgroups of Coxeter groups

John M. Burns
, Goetz Pfeiffer

Mathematics

University of Galway

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

In this note, we give a classification of the maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analog of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.

Original language	English
Pages (from-to)	114-120
Number of pages	7
Journal	Glasgow Mathematical Journal
Volume	65
Issue number	1
DOIs	https://doi.org/10.1017/S0017089522000143
Publication status	Published - 2 Jan 2023

Keywords

Coxeter groups
Lie algebras
root systems

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10.1017/S0017089522000143

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title = "Maximal order Abelian subgroups of Coxeter groups",

abstract = "In this note, we give a classification of the maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analog of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.",

keywords = "Coxeter groups, Lie algebras, root systems",

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AU - Pfeiffer, Goetz

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N2 - In this note, we give a classification of the maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analog of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.

AB - In this note, we give a classification of the maximal order Abelian subgroups of finite irreducible Coxeter groups. We also prove a Weyl group analog of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.

KW - Coxeter groups

KW - Lie algebras

KW - root systems

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DO - 10.1017/S0017089522000143

M3 - Article

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VL - 65

SP - 114

EP - 120

JO - Glasgow Mathematical Journal

JF - Glasgow Mathematical Journal

IS - 1

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Maximal order Abelian subgroups of Coxeter groups

Abstract

Keywords

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