On the quantum affine vertex algebra associated with trigonometric R-matrix

Slaven Kožic ^[1]
1. [1] University of Zagreb
  
  University of Zagreb
  
  Croacia
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 3, 2021
Idioma: inglés
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Resumen
- 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 (irreducible) ϕ-coordinated module for the level c∈C quantum affine vertex algebra is naturally equipped with a structure of (irreducible) restricted level c module for the quantum affine algebra in type A and vice versa. In the end, we discuss relation between the centers of the quantum affine algebra and the quantum affine vertex algebra.