Relative Garside elements of Artin monoids
Group Theory
2013-12-13 v1
Abstract
We introduce a relative Garside element, the quotient of the corresponding Garside elements G1 and G2, for a pair of Artin monoids associated to Coxeter graphs Gamma1 and Gamma2, the second graph containing a new vertex. These relative elements give a recurrence relation between Garside elements. As an application, we compute explicitly the Garside elements of Artin monoids corresponding to spherical Coxeter graphs or the longest elements of the associated finite Coxeter groups.
Keywords
Cite
@article{arxiv.1312.3411,
title = {Relative Garside elements of Artin monoids},
author = {Usman Ali and Barbu Berceanu and Zaffar Iqbal},
journal= {arXiv preprint arXiv:1312.3411},
year = {2013}
}
Comments
14 pages