## Higher Sugawara operators for the quantum affine algebras of type $$A$$

### Luc Frappat, Naihuan Jing, Alexander Molev and Eric Ragoucy

#### 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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 Friday, May 22, 2015