A poset connected to Artin monoids of simply laced type

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Abstract

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.
Original languageEnglish
Pages (from-to)1646-1666
JournalJournal of Combinatorial Theory, Series A
Volume113
Issue number8
DOIs
Publication statusPublished - 2006

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