Identical particles, exotic statistics and braid groups

The inequivalent quantizations of a system of n identical particles on a manifold M, dim M≥2, are in 1-1 correspondence with irreducible unitary representations of the braid group Bn(M). The notion of the statistics of the particles is made precise. We give various examples where all the possible statistics for the system are determined, and find instances where the particle obey statistics different from the well-studied Bose, Fermi para- and θ-statistics