Bosons and fermions. Quantum mechanics texts, such as Dirac's classic, explain that in a system of indistinguishable particles in space, exchange of particles is modelled by a change in phase of the state vector. These phases form a 1-dimensional representation of the symmetric group. Since all transpositions are conjugate, there are just two possibilities: bosons (trival rep) and fermions (sign rep), and no other(on)s.
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