On a family of nonparallel Regge trajectories

The paper is concerned with the occurrence of a family of parallel trajectories and is based on a group-theoretical approach to the problem of conspiring Regge trajectories. It is shown that for a definite class of groups, which includes $SO(4,2)$, It is impossible to construct a group-theoretical model that leads to a family of nonparallel trajectories. This result is obtained by studying the analytic properties of the functions in the integral formula that relates the matrix elements of the irreducible representations of these groups when restricted to the subgroup $SU(1,1)$ to the matrix elements of the representations of $SU(1,1)$.