仿射辛群作用下的面轨道生成的格

Lattices Generated by Orbits of Flats Under Finite Affine Symplectic Groups

设ASU(2v,F_q)是F_q上的2v维仿射辛空间,ASp_(2v)(F_q)是F_q上的2v次仿射辛群,设M(m,s)是ASp_(2v)(F_q)作用下的(m,s)面的轨道,用L(m,s)表示M(m,s)中面的交生成的集合.讨论了各轨道生成的集合之间的包含关系,一个面是由给定M(m,s)生成的集合中的一个元素的条件,以及L(m,s)何时做成几何格.

Let ASG （2v,Fq） be the 2v-dimensional affine symplectic space over the finite field Fq, let ASp2v（Fq） be the affine symplectic group of degree 2v over Fq ,M（m ,s） any orbit of （m ,s） flats in under ASG （2v,Fq）. Denote by L（rn,s） the sets of flats which are intersections of flats in M（m,s）, this paper discusses the relations of inclusion among sets generated by different orbits, a condition for which a flat is an element of set generated by the given orbit, and how the sets generated by orbits form the geometric lattices.