Higher Sugawara operators for the quantum affine algebras of type A

Alexander Molev; Eric Ragoucy; Luc Frappat; Naihuan Jing

Higher Sugawara operators for the quantum affine algebras of type A

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arxiv 1505.03667 v1 pith:S3JXVBXD submitted 2015-05-14 math.QA math-phmath.MPmath.RT

Luc Frappat , Naihuan Jing , Alexander Molev , Eric Ragoucy This is my paper · ORCID

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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.

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$Q$-operators, $q$-opers, and R-matrices in 5d $\mathcal{N}=1$ gauge theory
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