Quantum vertex algebra associated to quantum toroidal \mathfrakgl_N

2024/05/15 by Fulin Chen, Xin Huang, Chen, Fulin +5
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2405.09386

openalex publication_date 2024/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we associate the quantum toroidal algebra E_N of type \mathfrakgl_N with quantum vertex algebra through equivariant ϕ-coordinated quasi modules. More precisely, for every ℓ∈ ℂ, by deforming the universal affine vertex algebra of \mathfraksl_∞, we construct an ℏ-adic quantum \Z-vertex algebra V_\widehat\mathfraksl_∞,ℏ(ℓ,0). Then we prove that the category of restricted E_N-modules of level ℓ is canonically isomorphic to that of equivariant ϕ-coordinated quasi V_\widehat\mathfraksl_∞,ℏ(ℓ,0)-modules.

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