Visualizing conjugation in affine Coxeter groups
Group Theory
2026-05-29 v1
Abstract
Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Mili\'cevi\'c, Schwer and the second author, we develop an app to visualize conjugation in affine Coxeter groups in dimensions 2 and 3. The resulting pictures exhibit beautiful geometric symmetries.
Cite
@article{arxiv.2605.29337,
title = {Visualizing conjugation in affine Coxeter groups},
author = {Amy Herron and Anne Thomas},
journal= {arXiv preprint arXiv:2605.29337},
year = {2026}
}
Comments
10 pages, 4 figures, all in color