A Poset Connected to Artin Monoids of Simply Laced Type

Details A Poset Connected to Artin Monoids of Simply Laced Type A Poset Connected to Artin Monoids of Simply Laced Type

2005-02-24

arxiv.org/abs/math/0502501v1

Mathematics

Group Theory

Scientific paper

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 representatons 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.

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