Reflection subgroups of Coxeter groups

Felikson, Anna; Tumarkin, Pavel

doi:10.1090/S0002-9947-09-04859-4

Reflection subgroups of Coxeter groups
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by Anna Felikson and Pavel Tumarkin PDF

Trans. Amer. Math. Soc. 362 (2010), 847-858 Request permission

Abstract:

We use the geometry of the Davis complex of a Coxeter group to investigate finite index reflection subgroups of Coxeter groups. The main result is the following: if $G$ is an infinite indecomposable Coxeter group and $H\subset G$ is a finite index reflection subgroup, then the rank of $H$ is not less than the rank of $G$. This generalizes earlier results of the authors (2004). We also describe the relationship between the nerves of the group and the subgroup in the case of equal rank.

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