有限奇异辛群作用下(m,0,k)型子空间的子轨道(英文)

Suborbits of subspaces of type(m,0,k) underfinite singular symplectic groups

令F2ν+lq是有限域Fq上(2ν+l)维线性空间,Sp2ν+l,ν(Fq)是Fq上次数为(2ν+l)的奇异辛群。众所周知,在奇异辛空间中,所有的(m,0,k)型子空间构成的集合在奇异辛群的作用下形成一个轨道,主要得到了在这个作用下所有轨道的秩,并且计算了每个子轨道的长度。

Let Fq be the （2v ＋ 1）-dimensional vector space over the finite field Fq, and Sp2v ＋1 （ Fq ） the singular symplectie groups of degree 2v ＋ 1 over Fq. It is well known that the set of all the sub- spaces of type （ m,0, k） in a singular symplectic space forms an orbit under the action of the singular symplectic group. The ranks of all the orbitals under this action are determined, and the length of each suborbit is calculated.