Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra

[1910.04947] Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Quantum Algebra arXiv:1910.04947 (math) [Submitted on 11 Oct 2019 ( v1 ), last revised 22 Sep 2022 (this version, v3)] Title: Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra Authors: Sven Möller , Nils R. Scheithauer View a PDF of the paper titled Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra, by Sven M\"oller and 1 other authors View PDF HTML (experimental) Abstract: We prove a dimension formula for the weight-1 subspace of a vertex operator algebra $V^{\operatorname{orb}(g)}$ obtained by orbifolding a strongly rational, holomorphic vertex operator algebra $V$ of central charge 24 with a finite-order automorphism $g$. Based on an upper bound derived from this formula we introduce the notion of a generalised deep hole in $\operatorname{Aut}(V)$. Then we show that the orbifold construction defines a bijection between the generalised deep holes of the Leech lattice vertex operator algebra $V_\Lambda$ with non-trivial fixed-point Lie subalgebra and the strongly rational, holomorphic vertex operator algebras of central charge 24 with non-vanishing weight-1 space. This provides the first uniform construction of these vertex operator algebras and naturally generalises the correspondence between the deep holes of the Leech lattice $\Lambda$ and the 23 Niemeier lattices with non-vanishing root system found by Conway, Parker and Sloane. Comments: 50 pages, LaTeX; some changes to the exposition, numbering in Section 6 changed; to appear in Ann. of Math Subjects: Quantum Algebra (math.QA) ; Number Theory (math.NT); Representation Theory (math.RT) MSC classes: 17B69, 11F11, 11F27 Cite as: arXiv:1910.04947 [math.QA] (or arXiv:1910.04947v3 [math.QA] for this version) https://doi.org/10.48550/arXiv.1910.04947 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Ann. of Math., 197(1):221-288, 2023 Related DOI : https://doi.org/10.4007/annals.2023.197.1.4 Focus to learn more DOI(s) linking to related resources Submission history From: Sven Möller [ view email ] [v1] Fri, 11 Oct 2019 02:34:04 UTC (48 KB) [v2] Mon, 5 Oct 2020 14:36:48 UTC (51 KB) [v3] Thu, 22 Sep 2022 08:36:20 UTC (52 KB) Full-text links: Access Paper: View a PDF of the paper titled Dimension Formulae and Generalised Deep Holes of the Leech Lattice Vertex Operator Algebra, by Sven M\"oller and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.QA < prev | next > new | recent | 2019-10 Change to browse by: math math.NT math.RT 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

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