Boundary minimal models and the Rogers-Ramanujan identities

We determine when the irreducible modules L(cp, q, hm, n) over the simple Virasoro vertex algebras Virp, q, where p, q ≥ 2 are relatively prime with $0 < m < p$ and $0 < n < q$, are classically free. It turns out this only happens with the boundary minimal models, i.e., with the irreducible modules over Vir2, 2s + 1 for s ∈ Z₊. We thus obtain a complete description of the classical limits of these modules in terms of the jet algebra of the corresponding Zhu C₂-algebra. Gordon's generalization of the Rogers-Ramanujan identities is used in the proof, and our results in turn provide a natural interpretation of these identities.