Unified approach to quasi-particle excitations in the edge states of paired Hall states

We consider the edge states of the quantum Hall paired states, which were introduced as the ground-state wave function for (Formula presented) We propose that the paired Hall states such as the Haldane-Rezayi state and the Pfaffian state have the supersymmetry, and we clarify the exclusion statistics of the quasi-particle excitations. By use of an idea of the “restricted partition function” for the quasi-particle excitations and its relationship with the q-special functions, we explicitly compute the distribution functions for the quasi-particle. We also calculate the specific heat and show that our results coincide with previously reported results based on the conformal field theory. We further show that there is a duality between the Pfaffian state and the Haldane-Rezayi state.