Automorphisms of geometric structures associated to Coxeter groups

2012/02/29 by Graham White, White, Graham
Mathematics · #20F55 (Primary) 22F50 #20F65 (Secondary) #22D05 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F55 #msc:20F65 #msc:22D05 #msc:22F50

paper · pdf · doi:10.48550/arxiv.1202.6441

11 pages, 4 figures

arxiv created 2012/02/29 · arxiv updated 2012/03/01

Abstract

In this paper, we consider the automorphism groups of the Cayley graph with respect to the Coxeter generators and the Davis complex of an arbitrary Coxeter group. We determine for which Coxeter groups these automorphism groups are discrete. In the case where they are discrete, we express them as semidirect products of two obvious families of automorphisms. This extends a result of Haglund and Paulin.

Related

• On the non-discreteness of automorphism groups of Cayley graphs of Coxeter groups
• Automorphism groups of graphs
• A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes
• Automorphism groups of cyclic products of groups
• Automorphisms of Cayley graphs on generalised dicyclic groups