On inversion sets and the weak order in Coxeter groups
Group Theory
2016-05-10 v3 Combinatorics
Abstract
In this article, we investigate the existence of joins in the weak order of an infinite Coxeter group W. We give a geometric characterization of the existence of a join for a subset X in W in terms of the inversion sets of its elements and their position relative to the imaginary cone. Finally, we discuss inversion sets of infinite reduced words and the notions of biconvex and biclosed sets of positive roots.
Cite
@article{arxiv.1502.06926,
title = {On inversion sets and the weak order in Coxeter groups},
author = {Christophe Hohlweg and Jean-Philippe Labbé},
journal= {arXiv preprint arXiv:1502.06926},
year = {2016}
}
Comments
22 pages; 10 figures; v2 some references were added; v2: final version, to appear in European Journal of Combinatorics