On cycle decompositions in Coxeter groups
Group Theory
2016-11-11 v1
Abstract
The aim of this note is to show that the cycle decomposition of elements of the symmetric group admits a quite natural formulation in the framework of dual Coxeter theory, yielding a generalization of it to the family of so-called parabolic quasi-Coxeter elements of Coxeter groups (in the symmetric group every element is a parabolic quasi-Coxeter element). We show that such an element admits an analogue of the cycle decomposition. Elements which are not in this family still admit a generalized cycle decomposition, but it is not unique in general.
Cite
@article{arxiv.1611.03442,
title = {On cycle decompositions in Coxeter groups},
author = {Thomas Gobet},
journal= {arXiv preprint arXiv:1611.03442},
year = {2016}
}
Comments
10 pages