Construction géometrique de representations de Weil sur un corps fini

Details Construction géometrique de representations de Weil sur un corps fini Construction géometrique de representations de Weil sur un corps fini

1995-09-02

arxiv.org/abs/math/9509218v1

Mathematics

Representation Theory

Scientific paper

We construct, by contraction of a suitable complex vector bundle, the Weil representation of the finite symplectic group $Sp(A)$. We give an explicit description of the space of all lagrangian subspaces, which we use to compute the cocycle of our representation in terms of a geometric Gauss sum. We recover in this way previously constructed generalized Weil representations (see \cite{ast,cor}) by restriction of our representation to an appropiate embedding of $SL(n) $ into $Sp(A)$.

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