Boundary minimal models and the Rogers-Ramanujan identities
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918466775154688 |
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| author | Salazar, Diego |
| author_facet | Salazar, Diego |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundary minimal models and the Rogers-Ramanujan identities Salazar, Diego Quantum Algebra Combinatorics 17B69, 11P84 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. |
| title | Boundary minimal models and the Rogers-Ramanujan identities |
| topic | Quantum Algebra Combinatorics 17B69, 11P84 |
| url | https://arxiv.org/abs/2405.07126 |