Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials
You Gao, Hong You · Communications in Algebra · 2003
Let be the (2ν + l)-dimensional vector space over the finite field 𝔽 q , and Sp 2ν+l,ν(𝔽 q ) the singular symplectic groups of degree 2ν + l over 𝔽 q . Let ℳ be any orbit of subspaces under Sp 2ν+l,ν(𝔽 q ). Denote by ℒ the set of subspaces which are intersections of subspaces in ℳ and the intersection of the empty set of subspaces of is assumed to be . By ordering ℒ by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice ℒ, when the lattices form geometric lattice, and the characteristic polynomial of ℒ.