On the combinatorics of Forrester-Baxter models
Omar Foda, Trevor A. Welsh
Abstract
We provide further boson-fermion q-polynomial identities for the `finitised' Virasoro characters χp, p'r,s of the Forrester-Baxter minimal models M(p, p'), for certain values of r and s. The construction is based on a detailed analysis of the combinatorics of the set Pp, p'a, b, c(L) of q-weighted, length-L Forrester-Baxter paths, whose generating function χp, p'a, b, c(L) provides a finitisation of χp, p'r,s. In this paper, we restrict our attention to the case where the startpoint a and endpoint b of each path both belong to the set of Takahashi lengths. In the limit L -> infinity, these polynomial identities reduce to q-series identities for the corresponding characters.
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