In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” by Wang and Guo. The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic polynomials.
Xuemei Liu. "Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups." J. Appl. Math. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/732808