Mass spectra in the doubly symmetric theory of infinite-component fields

We consider the problem of the characteristics of mass spectra in the doubly symmetric theory of fields transforming under the proper Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible representations. We show that there exists a range of free parameters of the theory where the mass spectra of fermions are quite satisfactory from the physical standpoint and correspond to the picture expected in the parton model of hadrons.