Multinomials and polynomial bosonic forms for the branching functions of the su(2)M x su(2)N/su(2)M+N conformal coset models Original Research Article

We give explicit expressions for the q-multinomial generalizations of the q-binomials and Andrewsʹ and Baxterʹs q-trinomials. We show that the configuration sums for the generalized RSOS models in regime III studied by Date et al. can be expressed in terms of these multinomials. This generalizes the work of ABF and AB where configuration sums of statistical mechanical models have been expressed in terms of binomial and trinomial coefficients. These RSOS configuration sums yield the branching functions for the su(2)M x su(2)N/su(2)M+N coset models. The representation in terms of multinomials gives Rocha-Caridi-like formulas whereas the representatiot of Date et al. gives a double sum representation for the branching functions.