  We construct a covariant generating function for the spectrum of chiral
primaries of symmetric orbifold conformal field theories with N=(4,4)
supersymmetry in two dimensions. For seed target spaces K3 and T4, the
generating functions capture the SO(21) and SO(5) representation theoretic
content of the chiral ring respectively. Via string dualities, we relate the
transformation properties of the chiral ring under these isometries of the
moduli space to the Lorentz covariance of perturbative string partition
functions in flat space.
