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Higher Sugawara Operators for the Quantum Affine Algebras of Type A

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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 that 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 \({{\mathcal W}}\)-algebra of Frenkel and Reshetikhin.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique LAPTh, CNRS and Université de Savoie, BP 110, 74941, Annecy-le-Vieux Cedex, France

    Luc Frappat & Eric Ragoucy

  2. School of Mathematical Sciences, South China University of Technology, Guangzhou, 510640, Guangdong, China

    Naihuan Jing

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  4. School of Mathematics and Statistics, University of Sydney, Sydney, NSW, 2006, Australia

    Alexander Molev

Authors
  1. Luc Frappat
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  2. Naihuan Jing
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  3. Alexander Molev
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  4. Eric Ragoucy
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Corresponding author

Correspondence to Alexander Molev.

Additional information

Communicated by Y. Kawahigashi

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Frappat, L., Jing, N., Molev, A. et al. Higher Sugawara Operators for the Quantum Affine Algebras of Type A . Commun. Math. Phys. 345, 631–657 (2016). https://doi.org/10.1007/s00220-015-2566-7

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  • DOI: https://doi.org/10.1007/s00220-015-2566-7

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