For Coxeter groups $z^{|g|}$ is a coefficient of a uniformly bounded representation
Volume 174 / 2002
Fundamenta Mathematicae 174 (2002), 79-86
MSC: Primary 20F55, 22D99.
DOI: 10.4064/fm174-1-4
Abstract
We prove the theorem in the title by constructing an action of a Coxeter group on a product of trees.