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Automorphisms and opposition in twin buildings

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Abstract
We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2-spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an absolute point). Our results also hold for all finite irreducible spherical buildings of rank at least 3, and imply that every involution of a thick irreducible finite spherical building of rank at least 3 has a fixed residue.
Keywords
(B_N)-PAIR, spherical buildings, KAC-MOODY GROUPS, projective planes, twin buildings, COLLINEATIONS

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Citation

Please use this url to cite or link to this publication:

MLA
Devillers, Alice, James Parkinson, and Hendrik Van Maldeghem. “Automorphisms and Opposition in Twin Buildings.” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY 94.2 (2013): 189–201. Print.
APA
Devillers, A., Parkinson, J., & Van Maldeghem, H. (2013). Automorphisms and opposition in twin buildings. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 94(2), 189–201.
Chicago author-date
Devillers, Alice, James Parkinson, and Hendrik Van Maldeghem. 2013. “Automorphisms and Opposition in Twin Buildings.” Journal of the Australian Mathematical Society 94 (2): 189–201.
Chicago author-date (all authors)
Devillers, Alice, James Parkinson, and Hendrik Van Maldeghem. 2013. “Automorphisms and Opposition in Twin Buildings.” Journal of the Australian Mathematical Society 94 (2): 189–201.
Vancouver
1.
Devillers A, Parkinson J, Van Maldeghem H. Automorphisms and opposition in twin buildings. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. 2013;94(2):189–201.
IEEE
[1]
A. Devillers, J. Parkinson, and H. Van Maldeghem, “Automorphisms and opposition in twin buildings,” JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 94, no. 2, pp. 189–201, 2013.
@article{6834567,
  abstract     = {We show that every automorphism of a thick twin building interchanging the halves of the building maps some residue to an opposite one. Furthermore, we show that no automorphism of a locally finite 2-spherical twin building of rank at least 3 maps every residue of one fixed type to an opposite (a key step in the proof is showing that every duality of a thick finite projective plane admits an absolute point). Our results also hold for all finite irreducible spherical buildings of rank at least 3, and imply that every involution of a thick irreducible finite spherical building of rank at least 3 has a fixed residue.},
  author       = {Devillers, Alice and Parkinson, James and Van Maldeghem, Hendrik},
  issn         = {1446-7887},
  journal      = {JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY},
  keywords     = {(B_N)-PAIR,spherical buildings,KAC-MOODY GROUPS,projective planes,twin buildings,COLLINEATIONS},
  language     = {eng},
  number       = {2},
  pages        = {189--201},
  title        = {Automorphisms and opposition in twin buildings},
  url          = {http://dx.doi.org/10.1017/S1446788712000481},
  volume       = {94},
  year         = {2013},
}

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