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From $Q$-systems to quantum affine algebras and beyond

By Rinat Kedem

Also appears in collection : Cluster algebras: twenty years on / Vingt ans d'algèbres amassées

The theory of cluster algebras has proved useful in proving theorems about the characters of graded tensor products or Demazure modules, via the $Q$-system. Upon quantization, the algebra associated with this system is shown to be related to a quantum affine algebra. Graded characters are related to a polynomial representation of the quantum cluster variables. This immediately suggests a further deformation to the spherical DAHA, quantum toroidal algebras and elliptic Hall algebras.

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Citation data

  • DOI 10.24350/CIRM.V.19383803
  • Cite this video Kedem, Rinat (20/03/2018). From $Q$-systems to quantum affine algebras and beyond. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19383803
  • URL https://dx.doi.org/10.24350/CIRM.V.19383803

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