On the combinatorics of Forrester-Baxter models

TL;DR

This paper derives new boson-fermion q-polynomial identities for finitised Virasoro characters of Forrester-Baxter models, using combinatorics of specific paths, which in the limit yield known q-series identities.

Contribution

It introduces novel combinatorial constructions of finitised Virasoro characters for certain Forrester-Baxter models, focusing on paths with Takahashi length endpoints.

Findings

Derived new q-polynomial identities for finitised characters.

Connected polynomial identities to classical q-series identities.

Focused on paths with Takahashi length endpoints.

Abstract

We provide further boson-fermion q-polynomial identities for the `finitised' Virasoro characters \chi^{p, 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 P^{p, p'}_{a, b, c}(L) of q-weighted, length-L Forrester-Baxter paths, whose generating function \chi^{p, p'}_{a, b, c}(L) provides a finitisation of \chi^{p, 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.