Lattices generated by orbits of flats under finite affine-symplectic groups
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论文类型：期刊论文
发表时间：2009-08-01
发表刊物：LINEAR ALGEBRA AND ITS APPLICATIONS
收录刊物：EI、SCIE
卷号：431
期号：5-7
页面范围：536-542
ISSN号：0024-3795
关键字：Affine-symplectic group; Orbit; Geometric lattice
摘要：Let ASG(2v, F(q)) be the 2v-dimensional affine-symplectic space over the finite field F(q) and let ASp(2v)(F(q)) be the affine-symplectic group of degree 2v over Fq. For any two orbits M' and M '' of flats under ASP(2v)(F(q)), let L' (resp. L '')be the set of all flats which are joins (resp. intersections) of flats in M' (resp. M '') such that M '' subset of L' (resp. M' subset of L '') and assume the join (resp. intersection) of the empty set of flats in ASG(2v, F(q)) is 0(resp. F(q)((2v))). Let L = L' boolean AND L ''. By ordering L', L '', L by ordinary or reverse inclusion, six lattices are obtained. This article discusses when they form geometric lattices. (c) 2009 Elsevier Inc. All rights reserved.