Let ASG（2v ＋ l, v; Fq） be the （2v ＋l）-dimensional affine-singular symplectic space over the finite field Fq and ASp2v＋l,v（Fq） be the affine-singular symplectic group of degree 2v ＋ l over Fq. Let O be any or...Let ASG（2v ＋ l, v; Fq） be the （2v ＋l）-dimensional affine-singular symplectic space over the finite field Fq and ASp2v＋l,v（Fq） be the affine-singular symplectic group of degree 2v ＋ l over Fq. Let O be any orbit of flats under ASp2v＋l,v（Fq）. Denote by J the set of all flats which are joins of flats in O such that O LJ and assume the join of the empty set of flats in ASG（2v ＋ l, v;Fq） is φ. Ordering LJ by ordinary or reverse inclusion, then two lattices axe obtained. This paper firstly studies the inclusion relations between different lattices, then determines a characterization of flats contained in a given lattice LJ, when the lattices form geometric lattice, lastly gives the characteristic polynomial of LJ.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.61179026 and No.11701558
文摘Let ASG（2v ＋ l, v; Fq） be the （2v ＋l）-dimensional affine-singular symplectic space over the finite field Fq and ASp2v＋l,v（Fq） be the affine-singular symplectic group of degree 2v ＋ l over Fq. Let O be any orbit of flats under ASp2v＋l,v（Fq）. Denote by J the set of all flats which are joins of flats in O such that O LJ and assume the join of the empty set of flats in ASG（2v ＋ l, v;Fq） is φ. Ordering LJ by ordinary or reverse inclusion, then two lattices axe obtained. This paper firstly studies the inclusion relations between different lattices, then determines a characterization of flats contained in a given lattice LJ, when the lattices form geometric lattice, lastly gives the characteristic polynomial of LJ.
