Strongly convergent unitary representations of right-angled Artin groups
Abstract
We prove using a novel random matrix model that all right-angled Artin groups have a sequence of finite dimensional unitary representations that strongly converge to the regular representation. We deduce that this result applies also to: the fundamental group of a closed hyperbolic manifold that is either three dimensional or standard arithmetic type, any Coxeter group, and any word-hyperbolic cubulated group. One strong consequence of these results is that any closed hyperbolic three-manifold has a sequence of finite dimensional flat Hermitian vector bundles with bottom of the spectrum of the Laplacian asymptotically at least 1.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 7
- Pages
- 1305-1343
- Publication date
- 12 May 2026
- Language
- EN