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A lattice theoretical interpretation of generalized deep holes

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Authors : Lam, Ching Hung (Author of the conference)
CIRM (Publisher )

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Abstract : We will give a lattice theoretical interpretation of generalized deep holes of the Leech lattice VOA $V_\Lambda$. We show that a generalized deep hole defines a 'true' automorphism invariant deep hole of the Leech lattice. We will also discuss a correspondence between the set of isomorphism classes of holomorphic VOA $V$ of central charge $24$ having non-abelian $V_1$ and the set of equivalence classes of pairs $(\tau, \tilde{\beta})$ satisfying certain conditions, where $\tau\in Co_0$ and $\tilde{\beta}$ is a $\tau$-invariant deep hole of squared length $2$. It provides a new combinatorial approach towards the classification of holomorphic VOAs of central charge $24$. Finally, we will discuss an observation of G.Höhn, which relates the weight one Lie algebra of holomorphic VOAs of central charge $24$ to certain codewords associated with the glue codes of Niemeier lattices.

MSC Codes :
17B69 - Vertex operators; vertex operator algebras and related structures

Additional resources :
https://www.cirm-math.fr/RepOrga/2363/Slides/lam.pdf

    Information on the Video

    Film maker : Recanzone, Luca
    Language : English
    Available date : 04/07/2022
    Conference Date : 10/06/2022
    Subseries : Research talks
    arXiv category : Quantum Algebra
    Mathematical Area(s) : Algebra ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Video Time : 00:47:38
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2022-06-06_Hung_lam.mp4

Information on the Event

Event Title : Vertex Algebras and Representation Theory / Algèbres vertex et théorie des représentations
Event Organizers : Adamovic, Drazen ; Arakawa, Tomoyuki ; Moreau, Anne ; Scheithauer, Nils
Dates : 06/06/2022 - 10/06/2022
Event Year : 2022
Event URL : https://conferences.cirm-math.fr/2363.html

Citation Data

DOI : 10.24350/CIRM.V.19932703
Cite this video as: Lam, Ching Hung (2022). A lattice theoretical interpretation of generalized deep holes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19932703
URI : http://dx.doi.org/10.24350/CIRM.V.19932703

See Also

Bibliography

  • LAM, Ching Hung et MIYAMOTO, Masahiko. A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra. arXiv preprint arXiv:2205.04681, 2022. - https://arxiv.org/pdf/2205.04681.pdf



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