Quantum groups and nonabelian braiding in quantum Hall systems

Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyze the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localized 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 analyze the braid group representation carried by the multi-particle wave functions. As an application, we construct the nonabelian 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, recovering the results of C. Nayak and F. Wilczek for the Pfaffian state as a special case.