2N-QUASI-HOLE STATES REALIZE 2(N-1)-DIMENSIONAL SPINOR BRAIDING STATISTICS IN PAIRED QUANTUM HALL STATES

By explicitly identifying a basis valid for any number of electrons, w e demonstrate that simple multi-quasihole wave functions for the nu = 1/2 Pfaffian paired Hall state exhibit an exponential degeneracy at fi xed positions. Indeed, we conjecture that for 2n quasiholes the states realize a spinor representation of an expanded (continuous) non-Abeli an statistics group SO(2n), In the four-quasihole case, this is suppor ted by an explicit calculation of the corresponding conformal blocks i n the c = 1/2 + 1 conformal field theory. We present an argument for t he universality of this result, which is significant for the foundatio ns of fractional statistics generally. We note, for annular geometry, an amusing analog to black hole entropy. We predict, as a generic cons equence, glassy behavior, Many of our considerations also apply to a f orm of the (3, 3, 1) state.