Journal of Applied Mathematics

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

You Gao and XinZhi Fu

Full-text: Open access

Abstract

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

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 387132, 16 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495251

Digital Object Identifier
doi:10.1155/2012/387132

Mathematical Reviews number (MathSciNet)
MR2959992

Zentralblatt MATH identifier
1255.51002

Citation

Gao, You; Fu, XinZhi. Lattices Generated by Orbits of Subspaces under Finite Singular Orthogonal Groups II. J. Appl. Math. 2012 (2012), Article ID 387132, 16 pages. doi:10.1155/2012/387132. https://projecteuclid.org/euclid.jam/1355495251


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