The action of a Coxeter element on an affine root system
Combinatorics
2026-05-13 v3
Abstract
The characterization of orbits of roots under the action of a Coxeter element is a fundamental tool in the study of finite root systems and their reflection groups. This paper develops the analogous tool in the affine setting, adding detail and uniformity to a result of Dlab and Ringel.
Cite
@article{arxiv.1808.05090,
title = {The action of a Coxeter element on an affine root system},
author = {Nathan Reading and Salvatore Stella},
journal= {arXiv preprint arXiv:1808.05090},
year = {2026}
}
Comments
Version 1: This is a revised version of the first 1/3 of arXiv:1707.00340. (That paper will also be replaced by a new version, deleting the first 1/3 and with other major revisions). Version 2: Minor corrections to front and back matter. Version 3: Added mention of Dlab and Ringel, who proved essentially the same result in 1976 by a non-uniform argument