Non-Abelian statistics in the fractional quantum Hall states

The fractional quantum Hall states with non-Abelian statistics are studied. Those states are shown to be characterized by non-Abelian topological orders and are identified with some of the Jain states. The gapless edge states are found to be described by non-Abelian Kac-Moody algebras. It is argued that the topological orders and the associated properties are robust against any kinds of small perturbations.