Opposition diagrams for automorphisms of large spherical buildings

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:162

Article

关键词: Spherical building;    Opposition diagram;    Capped automorphism;    Domestic automorphims;    Displacement;   

DOI  :  10.1016/j.jcta.2018.09.011

来源: Elsevier

【 摘 要 】

Let theta be an automorphism of a thick irreducible spherical building Delta of rank at least 3 with no Fano plane residues. We prove that if there exist both type J(1) and J(2) simplices of Delta mapped onto opposite simplices by theta, then there exists a type J(1) boolean OR J(2) simplex of Delta mapped onto an opposite simplex by theta. This property is called cappedness. We give applications of cappedness to opposition diagrams, domesticity, and the calculation of displacement in spherical buildings. In a companion piece to this paper we study the thick irreducible spherical buildings containing Fano plane residues. In these buildings automorphisms are not necessarily capped. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free