On the Geometricity of Lattices Generated by Orbits of Subspaces Under Finite Classical Groups

AbstractLet Fnq be the n-dimensional vector space over the finite field Fq and let Gn be one of the classical groups of degree n over Fq. Let M be any orbit of subspaces under Gn. Denote by L the set of subspaces which are intersections of subspaces in M and assume the intersection of the empty set of subspaces of Fnq is Fnq itself. By ordering L by ordinary or reverse inclusion, two lattices are obtained. This paper discusses when they form geometric lattices