Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2009-08-01

Journal: LINEAR ALGEBRA AND ITS APPLICATIONS

Included Journals: EI、SCIE

Volume: 431

Issue: 5-7

Page Number: 536-542

ISSN: 0024-3795

Key Words: Affine-symplectic group; Orbit; Geometric lattice

Abstract: 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.