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 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. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.07126
- arXiv:
- arXiv:2405.07126
- Bibcode:
- 2024arXiv240507126S
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Combinatorics;
- 17B69;
- 11P84
- E-Print:
- 24 pages