Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

L. Bader; Maska Law; G. Lunardon; Tim Penttila; N. Ourante

doi:10.1023/A:1020878313625

Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

L. Bader, Maska Law, G. Lunardon, Tim Penttila, N. Ourante

Research output: Contribution to journal › Article

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	21-30
Journal	Journal of Algebraic Combinatorics
Volume	16
DOIs	https://doi.org/10.1023/A:1020878313625
Publication status	Published - 2002

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@article{073c210a359040699257ea31b1a873d1,

title = "Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems",

abstract = "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.",

author = "L. Bader and Maska Law and G. Lunardon and Tim Penttila and N. Ourante",

year = "2002",

doi = "10.1023/A:1020878313625",

language = "English",

volume = "16",

pages = "21--30",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer",

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TY - JOUR

T1 - Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems

AU - Bader, L.

AU - Law, Maska

AU - Lunardon, G.

AU - Penttila, Tim

AU - Ourante, N.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

U2 - 10.1023/A:1020878313625

DO - 10.1023/A:1020878313625

M3 - Article

VL - 16

SP - 21

EP - 30

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

ER -