Coxeter systems for which the Brink-Howlett automaton is minimal
arXiv:1811.06759
Abstract
In this article we classify the Coxeter systems for which the Brink-Howlett automaton is minimal. We show that this automaton is minimal if and only if each elementary root is supported on a standard spherical subsystem, thereby resolving a conjecture of Hohlweg, Nadeau and Williams.