Higher Sugawara operators for the quantum affine algebras of type A

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.

32 pages

References in corpus (3)

• Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence
• On higher order Sugawara operators
• A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra

Cited by in corpus (12)

• Center of the quantum affine vertex algebra in type A
• $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$
• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• Center of the quantum affine vertex algebra associated with trigonometric R-matrix
• Quasi modules for the quantum affine vertex algebra in type $A$
• Quantum current algebras associated with rational $R$-matrix
• Elliptic deformation of ${\mathcal{W}}_N$-algebras
• Higher order Hamiltonians for the trigonometric Gaudin model
• Center of the Yangian double in type A
• Generalized Yangians and their Poisson counterparts
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras
• Quantum Sugawara operators in type $A$