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- Title
AUTOMORPHISMS AND OPPOSITION IN TWIN BUILDINGS.
- Authors
DEVILLERS, ALICE; PARKINSON, JAMES; VAN MALDEGHEM, HENDRIK
- 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.
- Subjects
AUTOMORPHISMS; SPHERICAL buildings; POLYGONS; COXETER graphs; WEYL groups
- Publication
Journal of the Australian Mathematical Society, 2013, Vol 94, Issue 2, p189
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788712000481