Strongly convergent unitary representations of right-angled Artin groups

2023/08/01 by Magee, Michael, Thomas, Joe · 2 citations
#20F36 #22D10 #46L54 #58J50 #FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA) #Probability (math.PR) #Representation Theory (math.RT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2308.00863

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.

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