期刊论文

Nan, Jizhu

Nan, JZ (reprint author), Dalian Univ Technol, Dept Appl Math, Dalian 116024, Peoples R China.

Guo, Jun

2010-01-01

COMMUNICATIONS IN ALGEBRA

SCIE

J

38

6

2026-2036

0092-7872

Geometric lattice; Orbit; Singular symplectic group; Singular unitary group

be the n + l-dimensional vector space over a finite field F(q), and let G(n+l), (n) be the singular symplectic group Sp(n+ l, n)(F(q)) where n = 2v; or the singular unitary group U(n+l,n) (F(q)) where q = q(0)(2). For any two orbits M(1) and M(2) of subspaces under G(n+l, n), let L(1) (resp., L(2)) be the set of all subspaces which are sums (resp., intersections) of subspaces in M(1) (resp., M(2)) such that M(2) subset of L(1) (resp., M(1) subset of L(2)). Suppose L is the intersection of L(1) and L(2) containing {0} and F(q)(n+1). By ordering L by ordinary or reverse inclusion, two families of atomic lattices are obtained. This article characterizes the subspaces in the two lattices and classifies geometricity of these lattices.