Lattices generated by orbits of subspaces under finite singular pseudo-symplectic groups II

摘要

Let F_q~(2v+1+1) be the (2v + 1 + 1)-dimensional vector space over the finite field F_q. In the paper we assume that F_q is a finite field of characteristic 2, and Ps_(2v+1+1,2v+1)(F_q) the singular pseudo-symplectic groups of degree 2v + 1 + / over F_q. Let M be any orbit of subspaces under Ps_(2v+1+1,2v+1)(F_q)- Denote by C the set of subspaces which are intersections of subspaces in M and the intersection of the empty set of subspaces of F_q~(2v+1+1) is assumed to be F_q~(2v+1+1). By ordering C by ordinary or reverse inclusion, two lattices are obtained. This paper studies the questions when the lattices C form a geometric lattice.