有限酉群作用下子空间轨道按和生成的格

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 757-763.

有限酉群作用下子空间轨道按和生成的格

(1. 河北师范大学数学与信息科学学院河北石家庄 |050016; 2. $廊坊师范学院数学与信息科学学院河北廊坊 |065000|3. 北华航天工业学院基础部
河北廊坊 065000)

收稿日期:2007-12-09 修回日期:2009-02-08 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
河北省自然科学基金(A2005000141)、河北省教育厅自然科学基金(2007127, 2007137)、河北师范大学博士基金(L2004B04)和廊坊师范学院科学研究项目(LSAZ200702)资助

Lattices Generated by Joins of Elements in Orbits of Subspaces under Finite Unitary Groups

(1. Mathematics and Information College, Hebei Normal |University, Hebei Shijiazhuang 050016|2. Mathematics and Information College, Langfang Teachers' College, Hebei Langfang 065000|3. Department of Basic Courses, North |China |Institute |of |Astronautic |Engineering, Hebei Langfang 065000)

Received:2007-12-09 Revised:2009-02-08 Online:2009-06-25 Published:2009-06-25
Supported by:
河北省自然科学基金(A2005000141)、河北省教育厅自然科学基金(2007127, 2007137)、河北师范大学博士基金(L2004B04)和廊坊师范学院科学研究项目(LSAZ200702)资助

摘要/Abstract

摘要：

设F_q2⁽ⁿ⁾是 F_q2上的 n 维行向量空间, U_n( F_q2)是 F_q2上的 n 阶酉群. 设M(m, r; n)是U_n(F_q2}作用下的一个子空间轨道, L(m, r; n)是 M (m, r; n)中子空间的和生成的集合.该文讨论了各个轨道生成的集合L(m, r; n)之间的包含关系, 给出了一个子空间是属于给定的由M(m, r; n)生成的集合L(m, r, n)中的一个元素的条件, 以及L}(m, r; n)做成几何格的条件.

关键词: 酉群, 酉空间, 子空间轨道, 几何格

Abstract:

Let F_q2⁽ⁿ⁾ be the n-dimensional vector space over the finite field F_q2 and let U_n( F_q2) be unitary group of degree n over F_q2 . Let M(m, r; n) be any orbit of subspaces under U_n( F_q2}. Denote by L(m, r; n) the set of subspaces which are joins of subspaces in M(m, r; n) . This paper discusses the relation of inclusion between sets generated by different orbits, the condition that a subspace is an element of set generated by the given orbit, and the condition when sets generated by orbits form geometric lattices.

Key words: Unitary group, Unitary space, Orbit of subspaces, Geometric lattice

中图分类号:

06C10

张更生, 郭军, 张京轩. 有限酉群作用下子空间轨道按和生成的格[J]. 数学物理学报, 2009, 29(3): 757-763.

ZHANG Geng-Sheng, GUO Jun, ZHANG Jing-Xuan. Lattices Generated by Joins of Elements in Orbits of Subspaces under Finite Unitary Groups[J]. Acta mathematica scientia,Series A, 2009, 29(3): 757-763.

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