For right-angled Coxeter groups $z^ {\vert g\vert }$ is a coefficient of a uniformly bounded representation

Abstract:

A Coxeter group $\Gamma$ is right angled if any exponent in the Coxeter diagram is either $2$ or $\infty$. Using the action of $\Gamma$ on its Davis complex, we construct a family of cocycles that we use to perturb the left regular representation of $\Gamma$. In this way, we obtain a family ${({\pi _z})_{|z| < 1}}$ of uniformly bounded representations of $\Gamma$, of which the function $g \to |g|$ is a coefficient (where $|g|$ denotes the word length of $g \in \Gamma$).