Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-10-23
Nucl.Phys. B467 (1996) 247-271
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, no figures, latex; revised version to appear in Nucl. Phys. B, misprints eliminated, references updated
Scientific paper
10.1016/0550-3213(96)00103-4
We give explicit expressions for the q-multinomial generalizations of the q-binomials and Andrews' and Baxter's 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 $\widehat{su}(2)_{M}\times \widehat{su}(2)_{N}/\widehat{su}(2)_{M+N}$ coset models. The representation in terms of multinomials gives Rocha-Caridi like formulas whereas the representation of Date et al. gives a double sum representation for the branching functions.
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