Yangian characters and classical W-algebras

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.

43 pages

References in corpus (5)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators
• A new fusion procedure for the Brauer algebra and evaluation homomorphisms
• Path description of type B q-characters
• Casimir elements from the Brauer-Schur-Weyl duality

Cited by in corpus (7)

• Equivalences between three presentations of orthogonal and symplectic Yangians
• Jacobi-Trudi identity and Drinfeld functor for super Yangian
• Higher Sugawara operators for the quantum affine algebras of type A
• Classical W-algebras in types A, B, C, D and G
• Segal-Sugawara vectors for the Lie algebra of type $G_2$
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• On Segal--Sugawara vectors and Casimir elements for classical Lie algebras