Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $).

References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Groupes et algebres de Lie, Chapitres III-IV, Hermann, Paris, 1968. MR 0240238 (39:1590)
  • [2] M. Bożejko, T. Januszkiewicz, and R. Spatzier, Infinite Coxeter groups do not have the Kazhdan property $ T$, J. Operator Theory 19 (1988), 63-68. MR 950825 (89i:22025)
  • [3] M. Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983), 293-325. MR 690848 (86d:57025)
  • [4] M. Pimsner, Cocycles on trees, J. Operator Theory 17 (1987), 121-128. MR 873465 (88b:22020)
  • [5] T. Pytlik and R. Szwarc, An analytic family of uniformly bounded representation of free groups, Acta Math. 157 (1986), 287-309. MR 857676 (88e:22014)
  • [6] A. Valette, Cocycles d'arbres et representations uniforment bornees, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), 703-708. MR 1055232 (91i:22008)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20F55, 57M07

Retrieve articles in all journals with MSC: 20F55, 57M07

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society