On the combinatorics of Forrester-Baxter models

Details On the combinatorics of Forrester-Baxter models On the combinatorics of Forrester-Baxter models

2000-02-12

arxiv.org/abs/math/0002100v1

Physical combinatorics (Kyoto, 1999), 49--103, Progr. Math,. 191, Birkhauser, Boston, MA, 2000.

Mathematics

Quantum Algebra

63 pages, figures in eps format, LaTex, uses included Birkhauser macro, to appear in proceedings of "Physical Combinatorics",

Scientific paper

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.

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