在线阅读 --自然科学版 2009年1期《有限辛群作用下子空间轨道按和生成的格》
有限辛群作用下子空间轨道按和生成的格--[在线阅读]
郭军1, 张京轩2, 张更生3
1. 廊坊师范学院数学与信息科学学院, 河北廊坊 065000;
2. 北华航天工业学院基础部, 河北廊坊 065000;
3. 河北师范大学数学与信息科学学院, 河北石家庄 050016
起止页码: 4--12页
DOI:
摘要
Fq(2v)Fq上的2ν维行向量空间,Sp(Fq)是Fq上的2ν次辛群.设M(m,s;2ν)是Sp(Fq)作用下的一个子空间轨道,L(m,s;2ν)是M(m,s;2ν)中子空间的和生成的集合.讨论了在辛群作用下,各个轨道生成的集合L(m,s;2ν)之间的包含关系;一个子空间是由给定的M(m,s;2ν)生成的集合L(m,s;2ν)中的一个元素的条件;以及L(m,s;2ν)何时作成几何格.

Lattices Generated by Joins of Elements in Orbits of Subspaces Under Finite Symplectic Group
GUO Jun1, ZHANG Jing-xuan2, ZHANG Geng-sheng3
1. College of Mathematics and Information Science, Langfang Teachers' College, Hebei Langfang 065000, China;
2. Department of Basic Courses, North China Institute of Aerospace Engineering, Hebei Langfang 065000, China;
3. College of Mathematics and Information Science, Hebei Normal University, Hebei Shijiazhuang 050016, China
Abstract:
Let Fq(2v) be the 2ν-dimensional vector space over the finite field F/q and let Sp(Fq)be the symplectic group of degree 2νover Fq.Let M(m,s;2ν)be an orbit of subspaces under Sp(Fq).Let L(m,s;2ν) be the set of subspaces which are joins of subspaces in M(m,s;2ν).The relation of inclusion between sets generated by different orbits,the condition that a subspace is an elment of set generated by the given orbit,and when sets generated by orbits form geometric lat tices are discussed.

收稿日期: 2008-3-3
基金项目: 河北省自然科学基金(A2008000128);河北省教育厅科学研究基金(2007127,2008142);河北师范大学博士基金(L2004B04);廊坊师范学院科学研究项目(LSAZ200702)

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