  Following on from recent work describing the representation content of a
meromorphic bosonic conformal field theory in terms of a certain state inside
the theory corresponding to a fixed state in the representation, and using work
of Zhu on a correspondence between the representations of the conformal field
theory and representations of a particular associative algebra constructed from
it, we construct a general solution for the state defining the representation
and identify the further restrictions on it necessary for it to correspond to a
ground state in the representation space. We then use this general theory to
analyze the representations of the Heisenberg algebra and its $Z_2$-projection.
The conjectured uniqueness of the twisted representation is shown explicitly,
and we extend our considerations to the reflection-twisted FKS construction of
a conformal field theory from a lattice.
