Comments on Relativistic Supermultiplet Theories

It is proved that no well-behaved group of unitary operators on physical Hilbert space can have irreducible representations containing all spin states of the particles involved. It is shown that the recently proposed $U\left(12\right)\mathrm{}$ symmetry evades this theorem by acting on the "generalized $M$ function," rather than on the physical Hilbert space. Some other possible evasions are also discussed.