For right-angled Coxeter groups $z^ {\vert g\vert }$ is a coefficient of a uniformly bounded representation
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- by Tadeusz Januszkiewicz PDF
- Proc. Amer. Math. Soc. 119 (1993), 1115-1119 Request permission
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 $g \in \Gamma$).References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 1115-1119
- MSC: Primary 20F55; Secondary 57M07
- DOI: https://doi.org/10.1090/S0002-9939-1993-1172951-0
- MathSciNet review: 1172951