  We construct two infinite-dimensional irreducible representations for
$D(2,1;\alpha)$: a Schr\"odinger model and a Fock model. Further, we also
introduce an intertwining isomorphism. These representations are similar to the
minimal representations constructed for the orthosymplectic Lie supergroup and
for Hermitian Lie groups of tube type. The intertwining isomorphism is the
analogue of the Segal-Bargmann transform for the orthosymplectic Lie supergroup
and for Hermitian Lie groups of tube type.
