On the centre of Iwahori-Hecke algebras

Abstract

We prove triviality of the centre of arbitrary Hecke algebras of irreducible non-finite non-affine type. This result is obtained as a consequence of the following structure result for conjugacy classes of the underlying Coxeter groups. If $W$ is any infinite irreducible Coxeter group and $w \in W$ is a nontrivial element that is assumed not be a translation in case $W$ is affine, then there is an infinite sequence of conjugates of $w$ by Coxeter generators whose length is non-decreasing and tends to infinity.