中文摘要：

设F（q2ν＋l）是有限域Fq上的（2ν＋l）-维向量空间,Sp2ν＋l,ν（Fq）是Fq上2ν＋l级奇异辛群,M为Sp2ν＋l,ν（Fq）作用下的任一子空间轨道。LJ表示M中子空间的和的集合,并假定Fq（2ν＋l）的0个子空间的和是{0}子空间,按包含或反包含关系来定义LJ的偏序,可得两个格。研究了LJ的几何性。

英文摘要：

Let F（2ν＋l）q be the（2ν＋l）-dimensional vector space over the finite field Fq,and Sp2ν＋l,ν（Fq） the singular symplectic groups of degree 2ν＋l over Fq.Let M be any orbit of subspaces under Sp2ν＋l,ν（Fq）.Denote by LJ the set of subspaces which are joins of subspaces in M and the join of the empty set of subspaces of F（2ν＋l）q is assumed to be {0}.By ordering LJ by ordinary or reverse inclusion,two lattices are obtained.The questions when the lattices LJ form a geometric lattice is considered.