Symplectic polarities of buildings of type E₆
- Author
- Hendrik Van Maldeghem (UGent)
- Organization
- Abstract
- A symplectic polarity of a building Delta of type E (6) is a polarity whose fixed point structure is a building of type F (4) containing residues isomorphic to symplectic polar spaces. In this paper, we present two characterizations of such polarities among all dualities. Firstly, we prove that, if a duality theta of Delta never maps a point to a neighbouring symp, and maps some element to a non-opposite element, then theta is a symplectic duality. Secondly, we show that, if a duality theta never maps a chamber to an opposite chamber, then it is a symplectic polarity. The latter completes the programme for dualities of buildings of type E (6) of determining all domestic automorphisms of spherical buildings, and it also shows that symplectic polarities are the only polarities in buildings of type E (6) for which the Phan geometry is empty.
- Keywords
- Domestic automorphisms, Spherical buildings, Dualities of buildings of type E-6
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-3132665
- MLA
- Van Maldeghem, Hendrik. “Symplectic Polarities of Buildings of Type E₆.” DESIGNS CODES AND CRYPTOGRAPHY, vol. 65, no. 1–2, 2012, pp. 115–25, doi:10.1007/s10623-011-9573-2.
- APA
- Van Maldeghem, H. (2012). Symplectic polarities of buildings of type E₆. DESIGNS CODES AND CRYPTOGRAPHY, 65(1–2), 115–125. https://doi.org/10.1007/s10623-011-9573-2
- Chicago author-date
- Van Maldeghem, Hendrik. 2012. “Symplectic Polarities of Buildings of Type E₆.” DESIGNS CODES AND CRYPTOGRAPHY 65 (1–2): 115–25. https://doi.org/10.1007/s10623-011-9573-2.
- Chicago author-date (all authors)
- Van Maldeghem, Hendrik. 2012. “Symplectic Polarities of Buildings of Type E₆.” DESIGNS CODES AND CRYPTOGRAPHY 65 (1–2): 115–125. doi:10.1007/s10623-011-9573-2.
- Vancouver
- 1.Van Maldeghem H. Symplectic polarities of buildings of type E₆. DESIGNS CODES AND CRYPTOGRAPHY. 2012;65(1–2):115–25.
- IEEE
- [1]H. Van Maldeghem, “Symplectic polarities of buildings of type E₆,” DESIGNS CODES AND CRYPTOGRAPHY, vol. 65, no. 1–2, pp. 115–125, 2012.
@article{3132665,
abstract = {{A symplectic polarity of a building Delta of type E (6) is a polarity whose fixed point structure is a building of type F (4) containing residues isomorphic to symplectic polar spaces. In this paper, we present two characterizations of such polarities among all dualities. Firstly, we prove that, if a duality theta of Delta never maps a point to a neighbouring symp, and maps some element to a non-opposite element, then theta is a symplectic duality. Secondly, we show that, if a duality theta never maps a chamber to an opposite chamber, then it is a symplectic polarity. The latter completes the programme for dualities of buildings of type E (6) of determining all domestic automorphisms of spherical buildings, and it also shows that symplectic polarities are the only polarities in buildings of type E (6) for which the Phan geometry is empty.}},
author = {{Van Maldeghem, Hendrik}},
issn = {{0925-1022}},
journal = {{DESIGNS CODES AND CRYPTOGRAPHY}},
keywords = {{Domestic automorphisms,Spherical buildings,Dualities of buildings of type E-6}},
language = {{eng}},
number = {{1-2}},
pages = {{115--125}},
title = {{Symplectic polarities of buildings of type E₆}},
url = {{http://doi.org/10.1007/s10623-011-9573-2}},
volume = {{65}},
year = {{2012}},
}
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