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 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 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.Comment: 60 pages, 7 figures, LaTeX, uses AMSfont