Yangian characters and classical \(W\)-algebras

A. I. Molev and E. E. Mukhin

Abstract

The Yangian characters (or \(q\)-characters) are known to be closely related to the classical \(W\)-algebras and to the centers of the affine vertex algebras at the critical level. We make this relationship more explicit by producing families of generators of the \(W\)-algebras from the characters of the Kirillov-Reshetikhin modules associated with multiples of the first fundamental weight in types \(B\) and \(D\) and of the fundamental modules in type \(C\). We also give an independent derivation of the character formulas for these representations in the context of the RTT presentation of the Yangians. In all cases the generators of the \(W\)-algebras correspond to the recently constructed elements of the Feigin-Frenkel centers via an affine version of the Harish-Chandra isomorphism.