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Lattices generated by orbits of flats under finite affine-symplectic groups

✍ Scribed by Jun Guo; Jizhu Nan

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 142 KB
Volume: 431
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.03.002

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✦ Synopsis

Let ASG(2ν, F q ) be the 2ν-dimensional affine-symplectic space over the finite field F q and let ASp 2ν (F q ) be the affine-symplectic group of degree 2ν over F q . For any two orbits M and M of flats under ASp 2ν (F q ), let L (resp. L ) be the set of all flats which are joins (resp. intersections) of flats in M (resp. M ) such that M ⊆ L (resp. M ⊆ L ) and assume the join (resp. intersection) of the empty set of flats in ASG(2ν, F q ) is ∅ (resp. F (2ν) q ). Let L = L ∩ L . By ordering L , L , L by ordinary or reverse inclusion, six lattices are obtained. This article discusses when they form geometric lattices.

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