Abstract
For any nullity 2 extended affine Lie algebra ℰ of maximal type and ℓ ∈ ℂ, we prove that there exist a vertex algebra Vℰ(ℓ) and an automorphism group G of Vℰ(ℓ) equipped with a linear character χ, such that the category of restricted ℰ-modules of level ℓ is canonically isomorphic to the category of (G, χ)-equivariant ϕ-coordinated quasi Vℰ(ℓ)-modules. Moreover, when ℓ is a nonnegative integer, there is a quotient vertex algebra Lℰ(ℓ) of Vℰ(ℓ) modulo by a G-stable ideal, and we prove that the integrable restricted ℰ-modules of level ℓ are exactly the (G, χ)-equivariant ϕ-coordinated quasi-Lℰ(ℓ)-modules.
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Acknowledgement
This work was supported by the National Natural Science Foundation of China (Nos. 11971396, 11971397, 12131018, 12161141001), and the Fundamental Research Funds for the Central Universities (No. 20720200067). The authors would like to thank the Institute for Advanced Study in Mathematics, Zhejiang. Part of this work was carried out while the first and third authors were visiting the institute.
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Chen, F., Tan, S. & Yu, N. Extended affine Lie algebras, vertex algebras and equivariant ϕ-coordinated quasi-modules. Isr. J. Math. 259, 347–400 (2024). https://doi.org/10.1007/s11856-023-2488-6
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DOI: https://doi.org/10.1007/s11856-023-2488-6