2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55523In 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.LaTeX, 3 pagesHigh Energy Physics - TheoryCondensed Mattertext