Projective Statistics and Spinors in Hilbert Space
  In quantum mechanics, symmetry groups can be realized by projective, as well as by ordinary unitary, representations. For the permutation symmetry relevant to quantum statistics of N indistinguishable particles, the simplest properly projective representation is highly non-trivial, of dimension $2^{(N-1)/2}$, and is most easily realized starting with spinor geometry. Quasiparticles in the Pfaffian quantum Hall state realize this representation. Projective statistics is a consistent theoretical possibility in any dimension. 
Frank Wilczek