A superunitary Fock model of the exceptional Lie supergroup $\mathbb{D}(2,1;\alpha )$

We construct a Fock model of the minimal representation of the exceptional Lie supergroup $\mathbb{D}(2,1,\alpha )$. Explicit expressions for the action are given by integrating to group level a Fock model of the Lie superalgebra $D(2,1,\alpha )$ constructed earlier by the authors. It is also shown that the representation is superunitary in the sense of de Goursac–Michel.