Heterotic map on type II models and uniqueness of the partition function

We study the partition function of heterotic string models in any even space-time dimension which are obtained from type II models by a heterotic map. It is shown that if the original type II model has at least one space-time supersymmetry coming from the right moving sector then the number of fermions (respectively bosons) at each mass level is the same whether one uses SO(24+d) or E8xSO(8+d) characters to define the heterotic map. The partition functions of other models, constructed with some new group characters, are also shown to be equal to the previous ones. Results apply to Gepner's minimal N=2 constructions. (orig.)