The Perturbation ϕ2, 1 of the M(p, p + 1) Models of Conformal Field Theory and Related Polynomial-Character Identities

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 ϕ2, 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 Ap−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.