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Weak amenability of Coxeter groups

Gero Fendler
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Abstract

Let (G,S) be a Coxeter group. We construct a continuation, to the open unit disc, of the unitary representations associated to the positive definite functions g -> r^l(g). (Here 0<r<1, and l denotes the length function with respect to the generating set S.) The constructed representations are uniformly bounded and we prove that this implies the weak amenability of the group G.

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Gero Fendler. 2002-03-06. Weak amenability of Coxeter groups. https://arxiv.org/abs/math/0203052

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