Article ID Journal Published Year Pages File Type
4583469 Finite Fields and Their Applications 2009 10 Pages PDF
Abstract

Let be the n-dimensional vector space over a finite field Fq, and let Gn be the symplectic group Spn(Fq) where n=2ν; or the unitary group Un(Fq) where . For any two orbits M1 and M2 of subspaces under Gn, let L1 (resp. L2) be the set of all subspaces which are sums (resp. intersections) of subspaces in M1 (resp. M2) such that M2⊆L1 (resp. M1⊆L2). Suppose L is the intersection of L1 and L2 containing {0} and . By ordering L by ordinary or reverse inclusion, two families of atomic lattices are obtained. This article characterizes the subspaces in these lattices and classifies their geometricity.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory