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.