Journal of Statistical Physics, Vol. 82, Nos. 3/4. 1996. p. 657-685.
The problem of computing the one-dimensional configuration sums of the ABF model, in regime III is mapped onto the problem of evaluating the grandcanonical partition function of a gas of charged particles obeying certain
fermionic exclusion rules. We thus obtain a new fermionic method to compute the local height probabilities of the model. Combined with the original bosonic approach of Andrews, Baxter, and Forrester, we obtain a new proof of (some of) Melzer's polynomial identities. In the infinite limit these identities yield Rogers-Ramanujan type identities for the Virasoro characters ... as conjectured by the Stony Brook group. As a result of our work the corner transfer matrix and thermodynamic Bethe Ansatz approaches to solvable lattice models are unified.