Let k be an algebraically closed field of characteristic two. Let R be the ring of Witt vectors of length two over k. We construct a group stack \hat G over k, the metaplectic extension of the Greenberg realization of Sp_{ 2n}(R). We also construct a geometric analog of the Weil representation of \hat G, this is a triangulated category on which \hat G acts by functors. This triangulated category and the action are geometric in a suitable sense.
Categories: math.RT math.AG