We give a geometrical description of the spin-embedding esp of the symplectic dual polar space Δ∼= DW(5, 2r ) by showing how the natural embedding of W(5, 2r ) into PG(5, 2r ) is involved in the Grassmannembedding egr of Δ. We prove that the map sending every quad of Δ to its nucleus realizes the natural embedding of W(5, 2r ). Taking the quotient of egr over the space spanned by the nuclei of the quadrics corresponding to the quads of Δ gives an embedding isomorphic to esp.
A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3 / I., Cardinali; Lunardon, Guglielmo. - In: JOURNAL OF COMBINATORIAL THEORY. SERIES A. - ISSN 0097-3165. - STAMPA. - 115:(2008), pp. 1056-1064. [10.1016/j.jcta.2007.09.004]
A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3
LUNARDON, GUGLIELMO
2008
Abstract
We give a geometrical description of the spin-embedding esp of the symplectic dual polar space Δ∼= DW(5, 2r ) by showing how the natural embedding of W(5, 2r ) into PG(5, 2r ) is involved in the Grassmannembedding egr of Δ. We prove that the map sending every quad of Δ to its nucleus realizes the natural embedding of W(5, 2r ). Taking the quotient of egr over the space spanned by the nuclei of the quadrics corresponding to the quads of Δ gives an embedding isomorphic to esp.File | Dimensione | Formato | |
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