Quantum groups and non-Abelian braiding in quantum Hall systems

Wave functions describing quasiholes and electrons in non-Abelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localised particles carrying charges related to a quantum group that is determined explicitly for the cases of interest. The quantum group description naturally allows one to analyse the braid group representations carried by the multi-particle wave functions. As an application, we construct the non-Abelian braid group representations which govern the exchange of quasiholes in the fractional quantum Hall effect states that have been proposed by N. Read and E. Rezayi [Phys. Rev. B 59 (1999) 8084], recovering the results of C. Nayak and F. Wilczek [Nucl. Phys. B 479 (1996) 529] for the Pfaffian state as a special case