Periodicities of T-systems and Y-systems
Meeting Room 3, CMS
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]