2019/08/31 by Slaven Kožić
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine transformation #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Current algebra #Discrete mathematics #Filtered algebra #Geometry #Jordan algebra #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Quantum affine algebra #Quantum algebra #Quantum group #Trigonometry #Vertex (graph theory) #Vertex operator algebra #math-ph #math.MP #math.QA #math.RT #msc:17B37 #msc:17B69 #msc:81R50
paper · pdf · doi:10.1007/s00029-021-00666-x
published as Selecta Math. (N.S.) 27 (2021) 45 (49 pages) · 34 pages. Main Theorem extended to $\mathfrak{sl}_N$. Subsect.3.4 and Sect.4 added. Other minor changes. Comments are welcome
arxiv created 2020/01/21 · openalex publication_date 2021/06/11 · arxiv updated 2021/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We apply the theory of ϕ-coordinated modules, developed by H.-S. Li, to the Etingof--Kazhdan quantum affine vertex algebra associated with the trigonometric R-matrix of type A. We prove, for a certain associate ϕ of the one-dimensional additive formal group, that any ϕ-coordinated module for the level c∈ℂ quantum affine vertex algebra is naturally equipped with a structure of restricted level c module for the quantum affine algebra in type A and vice versa. Moreover, we show that any ϕ-coordinated module is irreducible with respect to the action of the quantum affine vertex algebra if and only if it is irreducible with respect to the corresponding action of the quantum affine algebra. In the end, we discuss relation between the centers of the quantum affine algebra and the quantum affine vertex algebra.