Lattices Generated by Orbits of Flats Under Finite Affine Groups
Kaishun Wang, Yan‐Quan Feng · Communications in Algebra · 2006
Let AG(n, q ) be the n-dimensional affine space over q . For a given integer m with 0 ≤ m ≤ n, all m-flats form an orbit, denoted by ℳ(m,n), under the action of the affine group AGL n ( q ) of AG(n, q ). Denote the set of all intersections of m-flats in ℳ(m,n) by ℒ(m,n). By ordering ℒ(m,n) by ordinary or reverse inclusion, two classes of lattices are obtained. This article discusses their geometricity, and computes their character polynomials.