Paths, Virasoro characters and fermionic expressions

Abstract

Baxter's corner transfer matrix method enables the one-point functions of certain 2D statistical models to be expressed as generating functions of weighted paths. In the case of the Forrester-Baxter models, the generating functions are Virasoro characters associated with the conformal minimal models M(p, p′). By combinatorially manipulating the paths, we obtain a quasiparticle description of the ensemble of paths. This directly leads to fermionic expressions for the Virasoro characters, and thence to interesting q-series identities.