Minimal representations of the metaplectic Lie supergroup and the super Segal-Bargmann transform

We construct a Schrödinger model and a Fock model of a minimal representation of the metaplectic Lie supergroup $\mathrm{M}\mathrm{p}(2m\mathrm{\mid }2n,2n)$. Then, we show that the Schrödinger model of the minimal representation leads to an already known Schrödinger model of the metaplectic representation of $\mathrm{M}\mathrm{p}(2m\mathrm{\mid }2n,2n)$. Therefore, the Fock model of the minimal representation allows us to construct a Fock model of this metaplectic representation. We then construct an intertwining super Segal-Bargmann transform which extends the classical Segal-Bargmann transform.