A Poset Connected to Artin Monoids of Simply Laced Type
Group Theory
2007-05-23 v1 Representation Theory
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 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.
Keywords
Cite
@article{arxiv.math/0502501,
title = {A Poset Connected to Artin Monoids of Simply Laced Type},
author = {A. M. Cohen and D. A. H. Gijsbers and D. B. Wales},
journal= {arXiv preprint arXiv:math/0502501},
year = {2007}
}