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# A poset connected to Artin monoids of simply laced type

@article{Cohen2006APC, title={A poset connected to Artin monoids of simply laced type}, author={Arjeh M. Cohen and Di{\'e} A. H. Gijsbers and David B. Wales}, journal={J. Comb. Theory, Ser. A}, year={2006}, volume={113}, pages={1646-1666} }

- Published 2006 in J. Comb. Theory, Ser. A
DOI:10.1016/j.jcta.2006.03.012

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representations of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset.