Boundary minimal models and the Rogers-Ramanujan identities
Abstract
We determine when the irreducible modules $L(c_{p, q}, h_{m, n})$ over the simple Virasoro vertex algebras $\operatorname{Vir}_{p, q}$, where $p, q \ge 2$ are relatively prime with $0 < m < p$ and $0 < n < q$, are classically free. It turns out that this only happens with the boundary minimal models, i.e., with the irreducible modules over $\operatorname{Vir}_{2, 2s + 1}$ for $s \in \mathbb{Z}_+$. We thus obtain a complete description of the classical limits of these modules in terms of the jet algebra of the corresponding Zhu $C_2$-algebra. The Andrews-Gordon generalization of the Rogers-Ramanujan identities is used in the proof, and our results in turn provide a natural interpretation of these identities.
Fields of Study & Subjects
Graph theory and applications
Advanced Mathematical Identities
Random Matrices and Applications
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 6
- Pages
- 108281–108281
- Publication date
- 29 April 2026
- Language
- EN