  Let F be a local field. In the case of F being the real field, Pierre Cartier
constructed Heisenberg-Weil representations of a Heisenberg group in families
using non-self-dual lattices. This result was later reformulated by Jae-Hyun
Yang in another paper. We extend this family of representations to a
representation of a Jacobi subgroup by incorporating a rational Metaplectic
group. In the case of F being a non-archimedean local field of odd residual
characteristic or a finite unramified extension of the field of 2-adic numbers,
we obtain similar results for a Jacobi group by incorporating a Metaplectic
group.
