## 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.

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 Tuesday, January 8, 2013