Uniclass automorphisms of spherical buildings
Group Theory
2024-03-27 v1
Abstract
An automorphism of a building is called uniclass if the Weyl distance between any chamber and its image lies in a single (twisted) conjugacy class of the Coxeter group. In this paper we characterise uniclass automorphisms of spherical buildings in terms of their fixed structure. For this purpose we introduce the notion of a Weyl substructure in a spherical building. We also link uniclass automorphisms to the Freudenthal--Tits magic square.
Cite
@article{arxiv.2403.17443,
title = {Uniclass automorphisms of spherical buildings},
author = {Yannick Neyt and James Parkinson and Hendrik Van Maldeghem},
journal= {arXiv preprint arXiv:2403.17443},
year = {2024}
}