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arXiv · 2403.17443

Uniclass automorphisms of spherical buildings

Yannick Neyt·James Parkinson·Hendrik Van Maldeghem
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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.

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Yannick Neyt, James Parkinson, Hendrik Van Maldeghem. 2024-03-26. Uniclass automorphisms of spherical buildings. https://arxiv.org/abs/2403.17443

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