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 analogue of Cartan's theorem that all maximal tori in a connected compact Lie group are conjugate.

shorter version with modified title and abstract. 9 pages; to appear in Glasgow Math. J