Lattices generated by joins of the flats in orbits under finite affine-singular symplectic group and its characteristic polynomials
type: Item
instance of: scholarly article
title: Lattices generated by joins of the flats in orbits under finite affine-singular symplectic group and its characteristic polynomials
zbMATH Open document ID: 1437.20042
author: You Gao
author: Yan-Yan Xue
author: Yuting Xiao
author: Xuemei Liu
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 2018-01-19T00:00:00Z
review text: Let ASG\((2\nu +l,\nu ;F_{q})\) be the \((2\nu +l)\)-dimensional affine-singular symplectic space over the finite field \(F_{q}\) and ASp\(_{2\nu +l,\nu }(F_{q}) \) be the affine-singular symplectic group of degree \(2\nu +l\) over \(F_{q}\). Let \(O\) be any orbit of flats under ASp\(_{2\nu +l,\nu }(F_{q})\). Denote by \( L^{J}\) the set of all flats which are joins of flats in \(O\) such that \( O\subseteq L^{J}\) and assume the join of the empty set of flats in ASp\( _{2\nu +l,\nu }(F_{q})\) is \(\emptyset \). Ordering \(L^{J}\) by ordinary or reverse inclusion, then two lattices are obtained. This paper firstly studies the inclusion relations between different lattices, then determines a characterization of flats contained in a given lattice \(L^{J}\), when the lattices form geometric lattices, lastly gives the characteristic polynomial of \(L^{J}\).
reviewed by: Nan Ji-Zhu
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 51D25
zbMATH DE Number: 6827828
zbMATH Keywords: lattice
zbMATH Keywords: affine-singular symplectic groups
zbMATH Keywords: characteristic polynomial
MaRDI profile type: Publication
full work available at URL: s10255-017-0707-9
OpenAlex ID: W2769635704
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DOI: 10.1007/S10255-017-0707-9
description: scientific article; zbMATH DE number 6827828