Computing reflection length in an affine Coxeter group

Joel Brewster Lewis, Jon McCammond, T. Kyle Petersen, Petra Schwer

Published 2017-10-18Version 1

In any Coxeter group, the conjugates of elements in its Coxeter generating set are called reflections and the reflection length of an element is its length with respect to this expanded generating set. In this article we give a simple formula that computes the reflection length of any element in any affine Coxeter group and we provide a simple uniform proof.