Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials
type: Item
instance of: scholarly article
title: Lattices generated by orbits of subspaces under finite singular unitary group and its characteristic polynomials
zbMATH Open document ID: 1025.20038
DOI: 10.1016/S0024-3795(02)00674-2
author: You Gao
published in: Linear Algebra and its Applications
publication date: 2003-07-30T00:00:00Z
review text: Let \(\mathbb{F}_{q^2}\) be a finite field with \(q^2\) elements and let \(\mathbb{F}_{q^2}^{n+l}\) be the \((n+l)\)-dimensional vector space over \(\mathbb{F}_{q^2}\). The singular unitary group \(U_{n+l,n}(\mathbb{F}_{q^2})\) of degree \(n+l\) over \(\mathbb{F}_{q^2}\) consists of all \((n+l)\times(n+l)\) matrices \(T\) such that \(TI_l\overline T^t=I_l\), where \(I_l=\left(\begin{smallmatrix} I^{(n)}&0\\ 0&0^{(l)}\end{smallmatrix}\right)\). A subspace \(P\) of \(\mathbb{F}_{q^2}^{n+l}\) is mapped into the subspace \(PT\) by \(T\in U_{n+l,n}\). The author also considers singular symplectic and singular orthogonal groups. Let \(\mathcal M\) be an orbit of subspaces and \(\mathcal L\) the set of subspaces that are intersections of subspaces of \(\mathcal M\). Ordering \(\mathcal L\) by ordinary or reverse inclusion produces two lattices. The author studies inclusion relations between lattices.
reviewed by: Erich W. Ellers
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 51D25
zbMATH DE Number: 1956804
zbMATH Keywords: geometric lattices
zbMATH Keywords: singular unitary groups
zbMATH Keywords: orbits of subspaces
zbMATH Keywords: singular symplectic groups
zbMATH Keywords: singular orthogonal groups
MaRDI profile type: Publication
cites work: Q3050437
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description: scientific article; zbMATH DE number 1956804