Higher Sugawara Operators for the Quantum Affine Algebras of Type A

Authors :: Luc Frappat
Eric Ragoucy
Alexander Molev
Naihuan Jing
Laboratoire d'Annecy-le-Vieux de Physique Théorique (LAPTH)
Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)
Source :: Communications in Mathematical Physics, Communications in Mathematical Physics, Springer Verlag, 2016, 345 (2), pp.631-657. ⟨10.1007/s00220-015-2566-7⟩, Communications in Mathematical Physics, Springer Verlag, 2016, 345, pp.631
Publication Year :: 2016
Publisher :: Springer Science and Business Media LLC, 2016.
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.<br />Comment: 32 pages

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