CONSTRUCTION GÉOMETRIQUE DE

REPRESENTATIONS DE WEIL SUR UN CORPS FINI

Jose Pantoja Jorge Soto-Andrade

Abstract. 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 [ast,cor]) by restriction of our representation to an appropiate embedding of SL(n) into Sp(A).

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