Center of the quantum affine vertex algebra associated with trigonometric $R$-matrix

Slaven Kožić and Alexander Molev

Abstract

We consider the quantum vertex algebra associated with the trigonometric $R$-matrix in type $A$ as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct an algebraically independent family of topological generators of the center at the critical level.