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On Opposition in Spherical Buildings and Twin Buildings

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Abstract.

In this paper, we prove a combinatorial property of twin apartments and opposition of chambers in twin buildings. We then characterize adjacency of chambers in twin buildings by meansof opposition of chambers. As an application, we study maps which satisfy certain conditions related to opposition of chambers, e.g., maps that preserve opposition. Applied to the special case of spherical buildings, all our main results as well as their corollaries are new.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany, e-mail: abramenk@mathematik.uni-bielefeld.de, , , , , , DE

    P. Abramenko

  2. Department of Pure Mathematics and Computer Algebra, University of Ghent, Galglaan 2, B-9000 Ghent, Belgium, e-mail: hvm@cage.rug.ac.be, , , , , , BE

    H. Van Maldeghem

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  1. P. Abramenko
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  2. H. Van Maldeghem
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Received February 20, 1999

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Abramenko, P., Van Maldeghem, H. On Opposition in Spherical Buildings and Twin Buildings. Annals of Combinatorics 4, 125–137 (2000). https://doi.org/10.1007/s000260050001

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  • DOI: https://doi.org/10.1007/s000260050001

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