2021/02/04 by Jeffrey Danciger, Danciger, Jeffrey, François Guéritaud +7 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2102.02757
openalex publication_date 2021/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate representations of Coxeter groups into GL(n,ℝ) as geometric reflection groups which are convex cocompact in the projective space ℙ(ℝn). We characterize which Coxeter groups admit such representations, and we fully describe the corresponding spaces of convex cocompact representations as reflection groups, in terms of the associated Cartan matrices. The Coxeter groups that appear include all infinite, word hyperbolic Coxeter groups; for such groups the representations as reflection groups that we describe are exactly the projective Anosov ones. We also obtain a large class of nonhyperbolic Coxeter groups, thus providing many examples for the theory of nonhyperbolic convex cocompact subgroups in ℙ(ℝn) developed in arXiv:1704.08711.