Geodesic
Flocks and partial flocks of hyperbolic quadrics via root systems
Journal of Algebraic Combinatorics, Tome 16 (2002) no. 1, pp. 21-30.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of $PG(3, q)$, for $q$ congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type $D _{4}, F _{4}, H _{4}$, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not being subflocks of linear flocks or of Thas flocks. We also give an alternative characterisation in terms of admitting a regular group fixing all the lines of one of the reguli of the hyperbolic quadric.
Keywords: flock, maximal exterior set, root system, rectangle condition, partial flock, exterior set, exceptional flock 
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     title = {Flocks and partial flocks of hyperbolic quadrics via root systems},
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Bader, Laura; Durante, Nicola; Law, Maska; Lunardon, Guglielmo; Penttila, Tim. Flocks and partial flocks of hyperbolic quadrics via root systems. Journal of Algebraic Combinatorics, Tome 16 (2002) no. 1, pp. 21-30. http://geodesic.mathdoc.fr/item/JAC_2002__16_1_a5/