Higher Sugawara operators for the quantum affine algebras of type \(A\)

Luc Frappat, Naihuan Jing, Alexander Molev and Eric Ragoucy

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.