## University of Sydney Algebra Seminar

# Alexander Molev (University of Sydney)

## Friday 10th August, 12:05-12:55pm, Carslaw 175

### Yangian characters and classical \(W\)-algebras

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 in types \(B\) and \(D\) and of the fundamental modules in type \(C\). 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.

This is joint work with Evgeny Mukhin.