Reflection subgroups of Coxeter groups

Felikson, Anna; Tumarkin, Pavel

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

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Journal article

Reflection subgroups of Coxeter groups

Felikson, Anna Independent University of Moscow, Russia - Department of Mathematics, University of Fribourg, Switzerland
Tumarkin, Pavel Independent University of Moscow, Russia - Department of Mathematics, Michigan State University, East Lansing, USA

18.09.2009

Published in:

Transactions of the American Mathematical Society. - 2010, vol. 362, p. 847-858.

English 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

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language