  Recent papers by Finkelstein, Galiautdinov, and coworkers {[J. Math. Phys.
42, 1489, 3299 (2001)]} discuss a suggestion by Wilczek that nonabelian
projective representations of the permutation group can be used as a new type
of particle statistics, valid in any dimension. Wilczek's suggestion was based
in part on an analysis by Nayak and Wilczek (NW) of the nonabelian
representation of the braid group in a quantum Hall system. We point out that
projective permutation statistics is not possible in a local quantum field
theory as it violates locality, and show that the NW braid group representation
is not equivalent to a projective representation of the permutation group. The
structure of the finite image of the braid group in a 2^{n/2-1}-dimensional
representation is obtained.
