Trouble with RelativisticSU(6)

Recently, several authors have proposed a relativistic generalization of the $\mathrm{SU}\left(6\right)\mathrm{}$ group, based on $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}$. The smallest group containing this group and the Poincaré group is found. This group has the catastrophic feature that all of its faithful unitary representations contain an infinite number of states for fixed four-momentum; thus there are an infinite number of particles in every supermultiplet. It is conjectured that similar difficulties afflict every group that contains an internal symmetry group and the Poincaré group in such a way that these groups do not commute. The conjecture is proven for a large class of Lie groups (semidirect products of semisimple groups and Abelian groups) under a restrictive assumption (that the translations are contained in the Abelian group).