AUTOMORPHISMS AND OPPOSITION IN TWIN BUILDINGS
ALICE DEVILLERS, JAMES PARKINSON, HENDRIK VAN MALDEGHEM
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Source: Crossref
Published: Mar 8, 2013
DOI: 10.1017/s1446788712000481
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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.
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