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The perturbation $ϕ_{2,1}$ of the M(p,p+1) models of conformal field theory and related polynomial character identities

Alexander Berkovich·Barry M. McCoy
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Abstract

Using $q$-trinomial coefficients of Andrews and Baxter along with the technique of telescopic expansions, we propose and prove a complete set of polynomial identities of Rogers-Ramanujan type for M(p, p+1) models of conformal field theory perturbed by the operator $phi_{2,1}$. The bosonic form of our polynomials is closely related to corner transfer matrix sums which arise in the computation of the order parameter in the regime $1^+$ of $A_{p-1}$ dilute models. In the limit where the degree of the polynomials tends to infinity our identities provide new companion fermionic representations for all Virasoro characters of unitary minimal series.

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Alexander Berkovich, Barry M. McCoy. 1998-09-17. The perturbation $ϕ_{2,1}$ of the M(p,p+1) models of conformal field theory and related polynomial character identities. https://arxiv.org/abs/math/9809066

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