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Normalizers of parabolic subgroups of Coxeter groups

Daniel Allcock

Algebraic & Geometric Topology 12 (2012) 1137–1143
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 D5 or Amodd 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