Lattices generated by orbits of subspaces under finite singular pseudo-symplectic groups. I.
type: Item
instance of: scholarly article
title: Lattices generated by orbits of subspaces under finite singular pseudo-symplectic groups. I.
zbMATH Open document ID: 1179.51005
author: You Gao
author: Juan Xu
published in: Linear Algebra and its Applications
publication date: 2009-09-14T00:00:00Z
review text: Let \(\mathbb{F}_q^{2\nu+1+l}\) be the \((2\nu+1+l)\)-dimensional vector space over the finite field \(\mathbb{F}_q\) of characteristic \(2\), and let \(Ps_{2\nu+1+l,2\nu+1}(\mathbb{F}_q)\) be the singular pseudo-symplectic group of degree \(2\nu+1+l\) over \(\mathbb{F}_q\). Let \(\mathcal{M}\) be any orbit of subspaces under \(Ps_{2\nu+1+l,2\nu+1}(\mathbb{F}_q)\). Denote by \(\mathcal{L}\) the set of subspaces that are intersections of subspaces in \(\mathcal{M}\). By ordering \(\mathcal{L}\) by ordinary or reverse inclusion, two lattices \(\mathcal{L_O}(\mathcal{M})\) and \(\mathcal{L_R}(\mathcal{M})\) are obtained. The authors investigate inclusion relations between different lattices, they give a characterization of subspaces contained in a given lattice \(\mathcal{L}\), and obtain the characteristic polynomial of \(\mathcal{L}\).
Mathematics Subject Classification ID: 51D25
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20H30
zbMATH DE Number: 5603565
zbMATH Keywords: lattice
zbMATH Keywords: singular pseudo-symplectic group
zbMATH Keywords: orbits of subspaces
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
full work available at URL: j.laa.2009.05.011
OpenAlex ID: W1997695061
cites work: Q3050437
cites work: Lattices generated by subspaces in \(d\)-bounded distance-regular graphs
cites work: Lattices Generated by Orbits of Flats Under Finite Affine Groups
cites work: Lattices generated by orbits of totally isotropic flats under finite affine-classical groups
cites work: Lattices generated by transitive sets of subspaces under finite classical groups I
cites work: Lattices generated by transitive sets of subspaces under finite classical groups II the orthogonal case of odd characteristic
cites work: Lattices generated by transitive sets of subspaces under finite classical groups III the orthogonal case of even characteristic
cites work: On the geometricity of lattices generated by orbits of subspaces under finite classical groups
cites work: Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials
cites work: Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials
DOI: 10.1016/J.LAA.2009.05.011
description: scientific article; zbMATH DE number 5603565