Non-Classical Hyperplanes of Finite Thick Dual Polar Spaces
We obtain a classification of the nonclassical hyperplanes of all finite thick dual polar spaces of rank at least 3 under the assumption that there are no ovoidal and semi-singular hex intersections. In view of the absence of known examples of ovoids and semi-singular hyperplanes in finite thick dual polar spaces of rank 3, the condition on the nonexistence of these hex intersections can be regarded as not very restrictive. As a corollary, we also obtain a classification of the nonclassical hyperplanes of $DW(2n-1,q)$, $q$ even. In particular, we obtain a complete classification of all nonclassical hyperplanes of $DW(2n-1,q)$ if $q \in \{ 8,32 \}$.
2017 ◽
Vol 16
(10)
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pp. 1750197
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2016 ◽
Vol 31
(17)
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pp. 1650102
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2003 ◽
Vol 35
(6)
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pp. 1059-1076
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2007 ◽
Vol 28
(7)
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pp. 1890-1909
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