Suborbits of \((m,k)\)-isotropic subspaces under finite singular classical groups
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 \(\mathcal M(2,0;4+\delta+l,4+\delta)\).
scientific article; zbMATH DE number 5693361