Normalizers of parabolic subgroups of Coxeter groups

Allcock, Daniel

doi:10.2140/agt.2012.12.1137

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Normalizers of parabolic subgroups of Coxeter groups

Daniel Allcock

Algebraic & Geometric Topology 12 (2012) 1137–1143

DOI: 10.2140/agt.2012.12.1137

Abstract

We improve a bound of Borcherds on the virtual cohomological dimension of the nonreflection part of the normalizer of a parabolic subgroup of a Coxeter group. Our bound is in terms of the types of the components of the corresponding Coxeter subdiagram rather than the number of nodes. A consequence is an extension of Brink’s result that the nonreflection part of a reflection centralizer is free. Namely, the nonreflection part of the normalizer of parabolic subgroup of type $D_{5}$ or $A_{m o d d}$ is either free or has a free subgroup of index $2$ .

Keywords

Coxeter group, parabolic subgroup, nonreflection part

Mathematical Subject Classification 2010

Primary: 20F55

References

Publication

Received: 13 September 2011

Accepted: 18 January 2012

Published: 22 May 2012

Authors

Daniel Allcock
Department of Mathematics University of Texas at Austin 1 University Station C1200 Austin TX 78712 USA
http://www.math.utexas.edu/~allcock

Volume 12, issue 2 (2012)