Vol. 12, No. 1, 2011

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Domesticity in projective spaces

Beukje Temmermans, Joseph A. Thas and Hendrik J. van Maldeghem

Vol. 12 (2011), No. 1, 141–149

Let J be a set of types of subspaces of a projective space. Then a collineation or a duality is called J-domestic if it maps no flag of type J to an opposite one. In this paper, we characterize symplectic polarities as the only dualities of projective spaces that map no chamber to an opposite one. This implies a complete characterization of all J-domestic dualities of an arbitrary projective space for all type subsets J. We also completely characterize and classify J-domestic collineations of projective spaces for all possible J.

symplectic polarity, displacement, projective spaces
Mathematical Subject Classification 2010
Primary: 51A10
Received: 10 September 2010
Accepted: 2 March 2011
Beukje Temmermans
Joseph A. Thas
Department of Mathematics
Ghent University
Krijgslaan 281
9000 Ghent
Hendrik J. van Maldeghem
Vakgroep Zuivere Wiskunde en Computeralgebra
University of Ghent
9000 Gent