Lattices Generated by Orbits of Flats Under Finite Affine Groups |
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| Authors: | Kaishun Wang Yan-quan Feng |
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| Affiliation: | 1. Department of Mathematics , Beijing Normal University , Beijing, China wangks@bnu.edu.cn;3. Department of Mathematics , Beijing Jiaotong University , Beijing, China |
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| Abstract: | 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,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,n) by ?(m,n). By ordering ?(m,n) by ordinary or reverse inclusion, two classes of lattices are obtained. This article discusses their geometricity, and computes their character polynomials. |
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| Keywords: | Affine group Flat Lattice |
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