Multinomials and polynomial bosonic forms for the branching functions of the (2) x (2)/(2) conformal coset models

1995/10/31 by Anne Schilling
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Binomial (polynomial) #Branching (polymer chemistry) #Combinatorics #Conformal map #Coset #Mathematical analysis #Mathematics #Multinomial distribution #Polynomial #Pure mathematics #Representation (politics) #Statistics #Trinomial #hep-th #math.QA #q-alg

paper · pdf · doi:10.1016/0550-3213(96)00103-4

published as Nucl.Phys. B467 (1996) 247-271 · 23 pages, no figures, latex; revised version to appear in Nucl. Phys. B, misprints eliminated, references updated

arxiv created 1996/03/27 · openalex publication_date 1996/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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 \widehatsu(2)_M× \widehatsu(2)_N/\widehatsu(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.

Citations

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