Lattices Generated by Orbits of Subspaces under Finite Singular Orthogonal Groups II
Keyword(s):
Let𝔽q(2ν+δ+l)be a(2ν+δ+l)-dimensional vector space over the finite field𝔽q. In this paper we assume that𝔽qis a finite field of odd characteristic, andO2ν+δ+l, Δ(𝔽q)the singular orthogonal groups of degree2ν+δ+lover𝔽q. Letℳbe any orbit of subspaces underO2ν+δ+l, Δ(𝔽q). Denote byℒthe set of subspaces which are intersections of subspaces inℳ, where we make the convention that the intersection of an empty set of subspaces of𝔽q(2ν+δ+l)is assumed to be𝔽q(2ν+δ+l). By orderingℒby ordinary or reverse inclusion, two lattices are obtained. This paper studies the questions when these latticesℒare geometric lattices.
2019 ◽
Vol 19
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pp. 2050086
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2011 ◽
Vol 85
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pp. 19-25
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2009 ◽
Vol DMTCS Proceedings vol. AK,...
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2019 ◽
Vol 53
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pp. 23-27
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2018 ◽
Vol 17
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pp. 1850189
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1998 ◽
Vol 65
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pp. 1-36
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