  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.
