Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials
Lattices Generated by Orbits of Subspaces Under Finite Singular Classical Groups and Its Characteristic Polynomials
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DOI：
10.1081/agb-120021900
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发表时间：
2003-01
影响因子：
0.7
通讯作者：
You Gao;H. You
中科院分区：
文献类型：
--
作者：
You Gao;H. You
摘要是（2ν + L） - 维矢量的（2ν + L）矢量空间𝔽 SP2ν+L，ν（𝔽Q）下的子空间。普通的或反向包含，获得了两个晶格，研究了不同晶格之间的包含关系，当晶格形成几何晶格和特征性的多项式ℒ时，给定晶格ℒ中包含的子空间的表征。
Abstract Let be the (2ν + l)-dimensional vector space over the finite field 𝔽 q , and Sp 2ν+l,ν(𝔽 q ) the singular symplectic groups of degree 2ν + l over 𝔽 q . Let ℳ be any orbit of subspaces under Sp 2ν+l,ν(𝔽 q ). Denote by ℒ the set of subspaces which are intersections of subspaces in ℳ and the intersection of the empty set of subspaces of is assumed to be . By ordering ℒ by ordinary or reverse inclusion, two lattices are obtained. This paper studies the inclusion relations between different lattices, a characterization of subspaces contained in a given lattice ℒ, when the lattices form geometric lattice, and the characteristic polynomial of ℒ.