Coxeter systems for which the Brink-Howlett automaton is minimal.

James Parkinson and Yeeka Yau

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.

Keywords: Coxeter group, root systems, elementary roots, automata, language of reduced words.

AMS Subject Classification: Primary 20E99.