Spin in the spectrum of states of dual models

The author considers the spectra of states of dual models, studying the helicity partition functions. These functions are generalizations of modular functions for an extension of the modular group. The spectra of the known models are rederived, and some further possibilities are considered. The singularities of the helicity partition functions yield the Regge trajectories of the models, including the newly discovered sister trajectories. (9 refs).