Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (3): 757-763.

• Articles • Previous Articles     Next Articles

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

  

  1. (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

Abstract:

Let Fq2(n) be the n-dimensional vector space over the finite field Fq2 and let   Un( Fq2) be  unitary group of degree n over Fq2 . Let M(m, r; n) be any orbit of subspaces under Un( Fq2}. 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

CLC Number: 

  • 06C10
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