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

Author: Tadeusz Januszkiewicz
Journal: Proc. Amer. Math. Soc. 119 (1993), 1115-1119
MSC: Primary 20F55; Secondary 57M07
MathSciNet review: 1172951
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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})_{\vert z\vert < 1}}$ of uniformly bounded representations of $ \Gamma $, of which the function $ g \to \vert g\vert$ is a coefficient (where $ \vert g\vert$ denotes the word length of $ g \in \Gamma $).

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Article copyright: © Copyright 1993 American Mathematical Society