Spectra of RSOS Soliton Theories

We study here the spectrum of soliton scattering theories based on interaction round the face lattice models. We take for the admissibility condition the fusion rules of each of the simple Lie algebras. It is found that the mass spectrum is given by that of the corresponding Toda theory, or, that the mass ratios of the different kinks in the model are described by the Perron--Frobenius vector of the Cartan matrix. The scalar part of the soliton amplitude is shown to be identical with the minimal part of the corresponding Toda amplitude.