The Weil Representation in Characteristic Two
نویسنده
چکیده
In this paper we construct a new variant of the Weil representation, associated with a symplectic vector space (V, ω) defined over a finite field of characteristic two. Our variant is a representation ρ : AMp (V ) → GL (H), where the group AMp (V ) is forth cover of a group ASp (V ), which is a nontrivial gluing of the symplectic group Sp (V ) and the dual group V ∗. In particular, the group ASp (V ) contains Weil’s pseudo-symplectic group as a strict subgroup. In the course, we develop the formalism of canonical vector spaces, which enables us to realize the group AMp (V ) and the representation ρ in a transparent manner.
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