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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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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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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