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

Abstract

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