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<p>An automorphism of a building is called <i>uniclass</i> 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 <i>Weyl substructure</i> in a spherical building. We also link uniclass automorphisms to the Freudenthal–Tits magic square.</p>

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Uniclass automorphisms of spherical buildings

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月12日

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  • Yannick Neyt,
  • James Parkinson,
  • Hendrik van Maldeghem

摘要

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.