[2405.07126] Boundary minimal models and the Rogers-Ramanujan identities Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:2405.07126 (math) [Submitted on 12 May 2024 ( v1 ), last revised 26 Apr 2026 (this version, v3)] Title: Boundary minimal models and the Rogers-Ramanujan identities Authors: Diego Salazar View a PDF of the paper titled Boundary minimal models and the Rogers-Ramanujan identities, by Diego Salazar View PDF HTML (experimental) 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. Comments: 21 pages Subjects: Quantum Algebra (math.QA) ; Combinatorics (math.CO) MSC classes: 17B69, 11P84 Cite as: arXiv:2405.07126 [math.QA] (or arXiv:2405.07126v3 [math.QA] for this version) https://doi.org/10.48550/arXiv.2405.07126 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Journal of Pure and Applied Algebra Volume 230, Issue 6, June 2026, 108281 Related DOI : https://doi.org/10.1016/j.jpaa.2026.108281 Focus to learn more DOI(s) linking to related resources Submission history From: Diego Salazar Gutierrez [ view email ] [v1] Sun, 12 May 2024 01:35:29 UTC (24 KB) [v2] Fri, 13 Feb 2026 02:09:40 UTC (52 KB) [v3] Sun, 26 Apr 2026 02:08:10 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Boundary minimal models and the Rogers-Ramanujan identities, by Diego Salazar View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2024-05 Change to browse by: math math.CO References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from