Quantum current algebras associated with rational R-matrix

2018/01/31 by Slaven Kožić
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Center (category theory) #Crystallography #Current algebra #Discrete mathematics #Jordan algebra #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum affine algebra #Quantum algebra #Quantum mechanics #Vertex (graph theory) #Vertex operator algebra #math-ph #math.MP #math.QA #math.RT

paper · pdf · doi:10.1016/j.aim.2019.05.031

published as Adv. Math. 351 (2019), 1072-1104 · 27 pages, minor changes and corrections, final version

arxiv created 2019/05/25 · openalex publication_date 2019/05/30 · arxiv updated 2019/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study quantum current algebra \textrmA(R) associated with the rational R-matrix of \mathfrakgl_N and we give explicit formulae for the elements of its center at the critical level. Due to Etingof--Kazhdan's construction, the level c vacuum module V_c(R) for the algebra \textrmA(R) possesses a quantum vertex algebra structure for any complex number c. We prove that any module for the quantum vertex algebra V_c(R) is naturally equipped with a structure of restricted \textrmA(R)-module of level c and vice versa.

Citations

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