Higher Sugawara operators for the quantum affine algebras of type A

TL;DR

This paper provides explicit formulas for central elements in quantum affine algebras of type A at the critical level, linking them to free field realizations and $q$-deformed $W$-algebras.

Contribution

It introduces explicit formulas for higher Sugawara operators and connects them with known realizations and $W$-algebras, advancing understanding of quantum affine algebra centers.

Findings

Explicit formulas for central elements at critical level

Images under Harish-Chandra homomorphism match free field realizations

Reproduction of generators of $q$-deformed classical $W$-algebra

Abstract

We give explicit formulas for the elements of the center of the completed quantum affine algebra in type $A$ at the critical level which are associated with the fundamental representations. We calculate the images of these elements under a Harish-Chandra-type homomorphism. These images coincide with those in the free field realization of the quantum affine algebra and reproduce generators of the $q$-deformed classical $W$-algebra of Frenkel and Reshetikhin.