Coxeter systems for which the Brink-Howlett automaton is minimal.
James Parkinson and Yeeka Yau
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.
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