We give a geometrical description of the spin-embedding $e_{sp}$ of the symplectic dual polar space $\Delta\cong DW(5,2^r)$ by showing how the natural embedding of $W(5,2^r)$ into $\PG(5,2^r)$ is involved in the Grassman-embedding $e_{gr}$ of $\Delta.$ We prove that the map sending every quad of $\Delta$ to its nucleus realizes the natural embedding of $W(5,2^r).$ Taking the quotient of $e_{gr}$ over the space spanned by the nuclei of the quadrics corresponding to the quads of $\Delta$ gives an embedding isomorphic to $e_{sp}.$

Cardinali, I., Lunardon, (2008). A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 115, 1056-1064 [10.1016/j.jcta.2007.09.004].

A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3

CARDINALI, ILARIA;
2008-01-01

Abstract

We give a geometrical description of the spin-embedding $e_{sp}$ of the symplectic dual polar space $\Delta\cong DW(5,2^r)$ by showing how the natural embedding of $W(5,2^r)$ into $\PG(5,2^r)$ is involved in the Grassman-embedding $e_{gr}$ of $\Delta.$ We prove that the map sending every quad of $\Delta$ to its nucleus realizes the natural embedding of $W(5,2^r).$ Taking the quotient of $e_{gr}$ over the space spanned by the nuclei of the quadrics corresponding to the quads of $\Delta$ gives an embedding isomorphic to $e_{sp}.$
2008
Cardinali, I., Lunardon, (2008). A geometric description of the spin-embedding of symplectic dual polar spaces of rank 3. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 115, 1056-1064 [10.1016/j.jcta.2007.09.004].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/18562
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