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

TL;DR

This paper studies the center of the quantum affine vertex algebra linked to the trigonometric R-matrix, proving its commutative structure and constructing generators at the critical level.

Contribution

It establishes the commutative nature of the center and provides an explicit algebraically independent generating set at the critical level.

Findings

Center is a commutative associative algebra

Constructed algebraically independent generators

Results apply to quantum vertex algebra of type A

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.