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On inclusions of exceptional long root geometries of type $\mathsf{E}$

Anneleen De Schepper and Hendrik Van Maldeghem

Vol. 20 (2023), No. 2-3, 247–293
Abstract

We prove the uniqueness of the inclusion of the long root geometries of type E6 and E7 as full embeddings in the one of type E8; the latter always arises as an equator geometry, the former as an intersection of two appropriate such equator geometries. Along the way, several other embedding results are obtained, notably featuring the subsequent point residuals of the above geometries.

Keywords
long root geometries, exceptional Tits buildings
Mathematical Subject Classification
Primary: 51E24
Secondary: 51B25
Milestones
Received: 9 August 2022
Revised: 8 November 2022
Accepted: 4 December 2022
Published: 13 September 2023
Authors
Anneleen De Schepper
Department of Mathematics: Algebra and Geometry
Ghent University
Ghent
Belgium
Hendrik Van Maldeghem
Department of Mathematics: Algebra and Geometry
Ghent University
Ghent
Belgium