有限奇异辛群作用下轨道中子空间的和生成的格(Ⅰ)(英文)  

Lattices generated by joins of the subspaces in orbits under finite singular symplectic groups(Ⅰ)

作　　者：高有[1] 付信志[1] 

机构地区：[1]中国民航大学理学院,天津300300

出　　处：《黑龙江大学自然科学学报》2009年第5期561-571,575,共12页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(60776810);the Natural Science Foundation of Tianjin City(08JCYBJC13900)

摘　　要：设Fq(2ν+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.研究了不同格之间的包含关系,含于一个给定的格LJ中的子空间的特征以及格LJ的特征多项式.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 inclusion relations between different lattices,a characterization of subspaces contained in a given lattice LJ,and the characteristic polynomial of LJ are studied.

关 键 词：格 奇异辛群 子空间轨道 子空间的和 

分 类 号：O157.4[理学—数学]