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Representation Theory, Mathematical Physics, and Integrable Systems pp 299–315Cite as

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Quantum Periodicity and Kirillov–Reshetikhin Modules

Part of the Progress in Mathematics book series (PM,volume 340)

Abstract

We give a proof of the periodicity of quantum T-systems of type A n × A ℓ with certain spiral boundary conditions. Our proof is based on the categorification of the T-system in terms of the representation theory of quantum affine algebras, more precisely on relations between classes of Kirillov–Reshetikhin modules and of evaluation modules.

To Nicolai Reshetikhin on his 60th birthday

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Acknowledgements

The author is very grateful to Bernard Leclerc for many discussions over the years and to Bernhard Keller for useful remarks and explanations about [Kel2] and its consequences. The author would like to thank Laura Fedele for her careful reading and for pointing typos in a former version of this work. The author is supported by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 Qaffine.

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Authors and Affiliations

  1. Université de Paris et Sorbonne Université, CNRS, IMJ-PRG, Paris, France

    David Hernandez

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  1. David Hernandez
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Correspondence to David Hernandez .

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Editors and Affiliations

  1. Section de Mathématiques, Université de Genève, Genève 4, Switzerland

    Prof. Anton Alekseev

  2. Department of Mathematics, University of California at Berkley, Berkeley, CA, USA

    Edward Frenkel

  3. Mathematics Department, Institut de Mathématiques de Jussieu, Paris Cedex 13, France

    Marc Rosso

  4. Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada

    Ben Webster

  5. Department of Mathematics, Northeastern University, Boston, MA, USA

    Prof. Milen Yakimov

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Hernandez, D. (2021). Quantum Periodicity and Kirillov–Reshetikhin Modules. In: Alekseev, A., Frenkel, E., Rosso, M., Webster, B., Yakimov, M. (eds) Representation Theory, Mathematical Physics, and Integrable Systems. Progress in Mathematics, vol 340. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-78148-4_10

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