点击次数：

论文类型：期刊论文

发表时间：2010-01-01

发表刊物：COMMUNICATIONS IN ALGEBRA

收录刊物：SCIE

卷号：38

期号：6

页面范围：2026-2036

ISSN号：0092-7872

关键字：Geometric lattice; Orbit; Singular symplectic group; Singular unitary group

摘要：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.