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Split buildings of type F₄ in buildings of type E₆

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Abstract
A symplectic polarity of a building of type is a polarity whose fixed point structure is a building of type containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type ). In this paper, we show in a geometric way that every building of type contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type fully embedded in the natural point-line geometry of arises from a symplectic polarity.
Keywords
EXCEPTIONAL GROUPS, LIE TYPE, SUBGROUPS, Buildings of exceptional type, Metasymplectic spaces, Point-line, geometries, Symplectic polarity

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MLA
De Schepper, Anneleen, et al. “Split Buildings of Type F₄ in Buildings of Type E₆.” ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, vol. 88, no. 1, 2018, pp. 97–160, doi:10.1007/s12188-017-0190-5.
APA
De Schepper, A., Sastry, N. N., & Van Maldeghem, H. (2018). Split buildings of type F₄ in buildings of type E₆. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 88(1), 97–160. https://doi.org/10.1007/s12188-017-0190-5
Chicago author-date
De Schepper, Anneleen, NS Narasimha Sastry, and Hendrik Van Maldeghem. 2018. “Split Buildings of Type F₄ in Buildings of Type E₆.” ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG 88 (1): 97–160. https://doi.org/10.1007/s12188-017-0190-5.
Chicago author-date (all authors)
De Schepper, Anneleen, NS Narasimha Sastry, and Hendrik Van Maldeghem. 2018. “Split Buildings of Type F₄ in Buildings of Type E₆.” ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG 88 (1): 97–160. doi:10.1007/s12188-017-0190-5.
Vancouver
1.
De Schepper A, Sastry NN, Van Maldeghem H. Split buildings of type F₄ in buildings of type E₆. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG. 2018;88(1):97–160.
IEEE
[1]
A. De Schepper, N. N. Sastry, and H. Van Maldeghem, “Split buildings of type F₄ in buildings of type E₆,” ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, vol. 88, no. 1, pp. 97–160, 2018.
@article{8566707,
  abstract     = {{A symplectic polarity of a building of type is a polarity whose fixed point structure is a building of type containing residues isomorphic to symplectic polar spaces (i.e., so-called split buildings of type ). In this paper, we show in a geometric way that every building of type contains, up to conjugacy, a unique class of symplectic polarities. We also show that the natural point-line geometry of each split building of type fully embedded in the natural point-line geometry of arises from a symplectic polarity.}},
  author       = {{De Schepper, Anneleen and Sastry, NS Narasimha and Van Maldeghem, Hendrik}},
  issn         = {{0025-5858}},
  journal      = {{ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG}},
  keywords     = {{EXCEPTIONAL GROUPS,LIE TYPE,SUBGROUPS,Buildings of exceptional type,Metasymplectic spaces,Point-line,geometries,Symplectic polarity}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{97--160}},
  title        = {{Split buildings of type F₄ in buildings of type E₆}},
  url          = {{http://doi.org/10.1007/s12188-017-0190-5}},
  volume       = {{88}},
  year         = {{2018}},
}

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