| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4602441 | Linear Algebra and its Applications | 2009 | 7 Pages |
Abstract
Let ASG(2ν,Fq) be the 2ν-dimensional affine-symplectic space over the finite field Fq and let ASp2ν(Fq) be the affine-symplectic group of degree 2ν over Fq. For any two orbits M′ and M″ of flats under ASp2ν(Fq), 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,Fq) is ∅ (resp. ). 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
