Weak amenability of Coxeter groups

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.

LaTex, 19 pages