Fused RSOS lattice models as higher-level nonunitary minimal cosets

Abstract

We consider the Forrester-Baxter RSOS lattice models with crossing parameter λ = (m'-m)π/m' in Regime III. In the continuum scaling limit, these models are described by the minimal models ℳ(m, m'). We conjecture that, for λ < π/n, the n ×n fused RSOS models with n ≥ 2 are described by the higher-level coset (A1(1))k ⊗ (A1(1))n/(A1(1))k+n at fractional level k = nM/(M'-M)-2 with (M, M') = (nm - (n - 1)m', m'). To support this conjecture, we investigate the one-dimensional sums arising from Baxter's off-critical corner transfer matrices. In unitary cases (m = m'-1) it is known that, up to leading powers of q, these coincide with the branching functions br,s,ℓm'-n, m', n(q). For general nonunit..