Lattices generated by orbits of subspaces under finite singular pseudo-symplectic groups I |
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Authors: | You Gao Juan Xu |
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Institution: | aCollege of Science, Civil Aviation University of China, Tianjin 300300, PR China;bDepartment of Mathematics, Linyi Normal University, Linyi, Shandong 276005, PR China |
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Abstract: | Let be the (2ν+1+l)-dimensional vector space over the finite field . In the paper we assume that is a finite field of characteristic 2, and the singular pseudo-symplectic groups of degree 2ν+1+l over . Let be any orbit of subspaces under . Denote by the set of subspaces which are intersections of subspaces in and the intersection of the empty set of subspaces of is assumed to be . By ordering 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 , and the characteristic polynomial of . |
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Keywords: | Lattice Singular pseudo-symplectic groups Orbit of subspaces |
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