论文信息 - Some remarks on the Spin Module Representation of Sp6(2e)

Some remarks on the Spin Module Representation of Sp6(2e)

We study the representation of a symplectic spread S of P G ( 5 , 2 e ) on the Grassmannian of the planes of P G ( 5 , 2 e ) . We observe that such a representation defines an ovoid of Q + ( 7 , 2 e ) which, in turn, via triality defines a spread of Q + ( 7 , 2 e ) one slice of which is isomorphic to S ; this allows to explicitly compute the ovoid of Q + ( 7 , 2 e ) without using a triality map. Also, we apply our arguments to show that a partial symplectic ovoid of P G ( 3 , 2 e ) defines a particular partial spread of Q + ( 7 , 2 e ) .

Guglielmo Lunardon | Laura Bader | L. Bader | G. Lunardon

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