  Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a
class of infinite-dimensional step 2 stratified Lie groups. We consider
holomorphic functions on $G$ that are square integrable with respect to a heat
kernel measure which is formally subelliptic, in the sense that all appropriate
finite dimensional projections are smooth measures. We prove a unitary
equivalence between a subclass of these square integrable holomorphic functions
and a certain completion of the universal enveloping algebra of the
"Cameron-Martin" Lie subalgebra. The isomorphism defining the equivalence is
given as a composition of restriction and Taylor maps.
