Lattices Generated by Orbits of Subspaces under Finite Singular Orthogonal Groups II

You Gao and XinZhi Fu

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

Abstract: Let 𝔽q(2ν+δ+l) be a (2ν + δ + l)‐dimensional vector space over the finite field 𝔽q. In this paper we assume that 𝔽q is a finite field of odd characteristic, and O2ν+δ+l, Δ(𝔽q) the singular orthogonal groups of degree 2ν + δ + l over 𝔽q. Let ℳ be any orbit of subspaces under O2ν+δ+l, Δ(𝔽q). Denote by ℒ the set of subspaces which are intersections of subspaces in ℳ, where we make the convention that the intersection of an empty set of subspaces of 𝔽q(2ν+δ+l) is assumed to be 𝔽q(2ν+δ+l). By ordering ℒ by ordinary or reverse inclusion, two lattices are obtained. This paper studies the questions when these lattices ℒ are geometric lattices.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:387132

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