Lattices generated by orbits of totally isotropic flats under finite affine-classical groups
The authors construct some families of finite atomic lattices \(\mathcal L\) generated by orbits of totally isotropic flats under finite affine-classical groups in the \(n\)-dimensional spaces \(ACG(n,F_q)\) over the finite field \(F_q\), namely the symplectic group, the unitary group, and the pseudo-symplectic group. \(\mathcal L\) denotes the set of all intersections of the elements of the corresponding orbits. The paper discusses their geometricity, and compute their characteristic polynomials.
scientific article; zbMATH DE number 5316914