1995/01/30 by Warnaar, S. O.
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.hep-th/9501134
The problem of computing the one-dimensional configuration sums of the ABF model in regime III is mapped onto the problem of evaluating the grand-canonical partition function of a gas of charged particles obeying certain fermionic exclusion rules. We thus obtain a new \em fermionic method to compute the local height probabilities of the model. Combined with the original \em 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 χ1,1(r-1,r)(q) as conjectured by the Stony Brook group. As a result of our working the corner transfer matrix and thermodynamic Bethe Ansatz approaches to solvable lattice models are unified.