A Schrödinger model, Fock model and intertwining Segal-Bargmann transform for the exceptional Lie superalgebra $D(2,1;\alpha )$

Sigiswald Barbier, Sam Claerebout

We construct two infinite-dimensional irreducible representations for $D(2,1;\alpha )$: a Schrödinger model and a Fock model. Further, we also introduce an intertwining isomorphism. Thes…