A Superunitary Fock Model of the Exceptional Lie Supergroup mathbb {D}(2, 1; alpha )

Abstract

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.