Canonical Reduction Systems in Artin-Tits groups of spherical type
Abstract
We introduce the canonical reduction system of an element in an Artin-Tits group of spherical type, which generalizes the similar notion for braids (and mapping classes) introduced by Birman, Lubotzky and McCarthy. We show its basic properties, which coincide with those satisfied in braid groups, and we provide an algorithm to compute it. We improve the algorithm in the case of braid groups, and discuss its complexity in this case. As a necessary result for obtaining the general algorithm, we prove that the centralizers of positive powers of an element form a periodic sequence and we show how to compute its period.
Keywords
Cite
@article{arxiv.2510.00713,
title = {Canonical Reduction Systems in Artin-Tits groups of spherical type},
author = {María Cumplido and Juan González-Meneses and Davide Perego},
journal= {arXiv preprint arXiv:2510.00713},
year = {2025}
}
Comments
30 pages, 3 figures. This version acknowledges an overlap with recent results by Kaitlin Ragosta, and includes the corresponding references