Center of the quantum affine vertex algebra in type A

TL;DR

This paper studies the center of the quantum affine vertex algebra in type A, proving its commutative structure and constructing independent generators at the critical level.

Contribution

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

Findings

Center is a commutative associative algebra

Constructed algebraically independent generators

Results are specific to type A quantum vertex algebra

Abstract

We consider the quantum vertex algebra associated with the double Yangian in type A as defined by Etingof and Kazhdan. We show that its center is a commutative associative algebra and construct algebraically independent families of topological generators of the center at the critical level.