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In Quantum field theory by Lewis H. Ryder, a supermultiplet is mentioned with no explanation as to what one is.

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A "multiplet" refers to an irreducible representation of some Lie group/algebra.

If it is the representation of some internal symmetry group, you get a multiplet of particles eg: the meson octet or the baryon decuplet are irreducible representations of SU(3) flavour symmetry. What that means is that under SU(3) flavour transformations, these particles/fields transform into each other and you cannot isolate or "reduce" the group to a subset that stays within itself under these transformations.

Similarly, a supermultiplet is a representation of the supersymmetry algebra under consideration.

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