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Buildings of exceptional type in a building of type E7

Anneleen De Schepper, N. S. Narasimha Sastry and Hendrik Van Maldeghem (UGent)
(2022) DISSERTATIONES MATHEMATICAE. 573. p.1-80
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Abstract
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.
Keywords
polar spaces, exceptional buildings, embeddings, fixed point structures, POLAR SPACES

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MLA
De Schepper, Anneleen, et al. “Buildings of Exceptional Type in a Building of Type E7.” DISSERTATIONES MATHEMATICAE, vol. 573, 2022, pp. 1–80, doi:10.4064/dm839-10-2021.
APA
De Schepper, A., Sastry, N. S. N., & Van Maldeghem, H. (2022). Buildings of exceptional type in a building of type E7. DISSERTATIONES MATHEMATICAE, 573, 1–80. https://doi.org/10.4064/dm839-10-2021
Chicago author-date
De Schepper, Anneleen, N. S. Narasimha Sastry, and Hendrik Van Maldeghem. 2022. “Buildings of Exceptional Type in a Building of Type E7.” DISSERTATIONES MATHEMATICAE 573: 1–80. https://doi.org/10.4064/dm839-10-2021.
Chicago author-date (all authors)
De Schepper, Anneleen, N. S. Narasimha Sastry, and Hendrik Van Maldeghem. 2022. “Buildings of Exceptional Type in a Building of Type E7.” DISSERTATIONES MATHEMATICAE 573: 1–80. doi:10.4064/dm839-10-2021.
Vancouver
1.
De Schepper A, Sastry NSN, Van Maldeghem H. Buildings of exceptional type in a building of type E7. DISSERTATIONES MATHEMATICAE. 2022;573:1–80.
IEEE
[1]
A. De Schepper, N. S. N. Sastry, and H. Van Maldeghem, “Buildings of exceptional type in a building of type E7,” DISSERTATIONES MATHEMATICAE, vol. 573, pp. 1–80, 2022.
@article{8745690,
  abstract     = {{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.}},
  author       = {{De Schepper, Anneleen and Sastry, N. S. Narasimha and Van Maldeghem, Hendrik}},
  issn         = {{0012-3862}},
  journal      = {{DISSERTATIONES MATHEMATICAE}},
  keywords     = {{polar spaces,exceptional buildings,embeddings,fixed point structures,POLAR SPACES}},
  language     = {{eng}},
  pages        = {{1--80}},
  title        = {{Buildings of exceptional type in a building of type E7}},
  url          = {{http://doi.org/10.4064/dm839-10-2021}},
  volume       = {{573}},
  year         = {{2022}},
}
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