✦ LIBER ✦
On the Geometricity of Lattices Generated by Orbits of Subspaces Under Finite Classical Groups
✍ Scribed by Yuanji Huo; Zhe-Xian Wan
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 165 KB
- Volume
- 243
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let n q be the n-dimensional vector space over the finite field q and let G n be one of the classical groups of degree n over q . Let be any orbit of subspaces under G n . Denote by the set of subspaces which are intersections of subspaces in and assume the intersection of the empty set of subspaces of n q is n q itself. By ordering by ordinary or reverse inclusion, two lattices are obtained. This paper discusses when they form geometric lattices.