Suborbits of \((m,k)\)-isotropic subspaces under finite singular classical groups
type: Item
instance of: scholarly article
title: Suborbits of \((m,k)\)-isotropic subspaces under finite singular classical groups
zbMATH Open document ID: 1201.05104
author: Jun Guo
published in: Finite Fields and their Applications
publication date: 2010-04-15T00:00:00Z
review text: Let \(\mathbb F_q^{2\nu+\delta+l}\) be one of the \((2\nu+\delta+l)\)-dimensional singular classical spaces and \(G_{2\nu+\delta+l,2\nu+\delta}\) be the corresponding singular classical group of degree \(2\nu+\delta+l\), then there is an action of the singular classical group \(G_{2\nu+\delta+l,2\nu+\delta}\) on the singular classical spaces \(\mathbb F_q^{2\nu+\delta+l}\). In this paper, the authors determine all the orbitals and the rank of \((G_{2\nu+\delta+l,2\nu+\delta}, \mathcal M(m,k;2\nu+\delta+l,2\nu+\delta))\), and they also compute all the intersection numbers of the symmetric association scheme \(\mathcal M(\nu+k,k;2\nu+\delta+l,2\nu+\delta,\Lambda))\), where \(k=1\) or \(k=l-1\). Furthermore, they construct a family of symmetric graphs with diameter 2 based on \(\mathcal M(2,0;4+\delta+l,4+\delta)\).
reviewed by: Nan Ji-Zhu
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51D25
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 5693361
zbMATH Keywords: singular classical group
zbMATH Keywords: isotropic subspace
zbMATH Keywords: suborbit
MaRDI profile type: Publication
full work available at URL: j.ffa.2009.11.001
OpenAlex ID: W2053783490
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DOI: 10.1016/J.FFA.2009.11.001
description: scientific article; zbMATH DE number 5693361