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Indexed by:期刊论文

Date of Publication:2010-01-01

Journal:COMMUNICATIONS IN ALGEBRA

Included Journals:SCIE

Volume:38

Issue:6

Page Number:2026-2036

ISSN No.:0092-7872

Key Words:Geometric lattice; Orbit; Singular symplectic group; Singular unitary group

Abstract: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.