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Periodicities of T-systems and Y-systems

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Discrete Integrable Systems

The T and Y-systems originate in conformal field theory and Bethe ansatz studies of solvable lattice models during 80’s-90’s. They are difference equations of Hirota-Miwa or Toda type that possess a variety of aspects related to dilogarithm identity, Kirillov-Reshetikhin conjecture, q-character of quantum affine algebras and so forth. More recently, there has been a renewed interest in their connection to the cluster algebras of Fomin-Zelevinsky, the cluster category of Buan-Marsh-Reineke-Reiten-Todorov and the periodicity conjecture by Zamolodchikov and others. I shall give an introductory overview on these topics. [joint work with R.Inoue, O.Iyama, B.Keller, T.Nakanishi and J.Suzuki]

This talk is part of the Isaac Newton Institute Seminar Series series.

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