My understanding is that when it comes to the correspondence between representation theory and particle physics, every irreducible representation of the Poincare group has a corresponding fundamental particle.
My questions are as follows:
are all of the currently known fundamental particles predicted to exist by this correspondence idea?
does the traditional $ISO(3,1)$ Poincare group/algebra predict the existence of supersymmetric particles? If not, what superalgebra is needed?