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Buildings of exceptional type in a building of type E7

Journal Contribution - Journal Article

We investigate the possible ways in which a thick metasymplectic space 1", that is, a Lie incidence geometry of type F4,1 (or F4,4), is embedded into the long root geometry Delta related to any building of type E7. We provide a complete classification (if 1" is not embedded in a singular subspace). As an application we prove the uniqueness of the inclusion of the long root geometry of type E6 in the one of type E7; it always arises as an equator geometry. We also use the latter concept to geometrically construct one of the embeddings turning up in our classification. As a side result we find that all triples of pairwise opposite elements of type 7 in a building of type E7 are projectively equivalent.
ISSN: 1730-6310
Volume: 573
Number of pages: 1
Publication year:2022
Embargoed until:01/09/2022