Polarized non-abelian representations of slim near-polar spaces |
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Authors: | Bart De Bruyn Binod Kumar Sahoo |
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Institution: | 1.Department of Mathematics,Ghent University,Gent,Belgium;2.School of Mathematical Sciences,National Institute of Science Education and Research,Odisha,India |
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Abstract: | In (Bull Belg Math Soc Simon Stevin 4:299–316, 1997), Shult introduced a class of parapolar spaces, the so-called near-polar spaces. We introduce here the notion of a polarized non-abelian representation of a slim near-polar space, that is, a near-polar space in which every line is incident with precisely three points. For such a polarized non-abelian representation, we study the structure of the corresponding representation group, enabling us to generalize several of the results obtained in Sahoo and Sastry (J Algebraic Comb 29:195–213, 2009) for non-abelian representations of slim dense near hexagons. We show that with every polarized non-abelian representation of a slim near-polar space, there is an associated polarized projective embedding. |
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