Local recognition of the point graphs of some Lie incidence geometries

Given a finite Lie incidence geometry which is either a polar space of rank at least \(3\) or a strong parapolar space of symplectic rank at least \(4\) and diameter at most \(4\), or the parapolar space arising from the line Grassmannian of a projective space of dimension at least \(4\), we show th...

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Bibliographic Details
Published inarXiv.org
Main Authors Ihringer, Ferdinand, Jansen, Paulien, Lambrecht, Linde, Neyt, Yannick, Rijpert, Daan, Hendrik Van Maldeghem, Victoor, Magali
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.10.2023
Subjects
Diameters
Differential geometry
Graphs
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Summary:Given a finite Lie incidence geometry which is either a polar space of rank at least \(3\) or a strong parapolar space of symplectic rank at least \(4\) and diameter at most \(4\), or the parapolar space arising from the line Grassmannian of a projective space of dimension at least \(4\), we show that its point graph is determined by its local structure. This follows from a more general result which classifies graphs whose local structure can vary over all local structures of the point graphs of the aforementioned geometries. In particular, this characterises the strongly regular graphs arising from the line Grassmannian of a finite projective space, from the half spin geometry related to the quadric \(Q^+(10,q)\) and from the exceptional group of type \(\mathsf{E_6}(q)\) by their local structure.
ISSN:2331-8422