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Quantum Affine Algebras and Cluster Algebras

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Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Part of the book series: Progress in Mathematics ((PM,volume 337))

Abstract

This article is an extended version of the minicourse given by the second author at the summer school of the conference Interactions of quantum affine algebras with cluster algebras, current algebras and categorification, held in June 2018 in Washington. The aim of the minicourse, consisting of three lectures, was to present a number of results and conjectures on certain monoidal categories of finite-dimensional representations of quantum affine algebras, obtained by exploiting the fact that their Grothendieck rings have the natural structure of a cluster algebra.

To Vyjayanthi Chari on her birthday

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Notes

  1. 1.

    In these lectures, we will only consider type I representations of quantum enveloping algebras. All representations can be obtained from the type I representations by twisting with some signs, see e.g. [4, §10.1].

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Acknowledgements

D. Hernandez is supported in part by the European Research Council under the European Union’s Framework Programme H2020 with ERC Grant Agreement number 647353 QAffine.

Author information

Authors and Affiliations

  1. Université de Paris, Univ Paris Diderot, CNRS Institut de Mathématiques de Jussieu-Paris Rive Gauche UMR 7586, Paris, France

    David Hernandez

  2. Institut Universitaire de France, Paris, France

    David Hernandez

  3. Normandie Univ, UNICAEN, CNRS, LMNO, Caen, France

    Bernard Leclerc

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  1. David Hernandez
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Correspondence to Bernard Leclerc .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Riverside, Riverside, CA, USA

    Jacob Greenstein

  2. IMJ-PRG, Université de Paris, Paris, France

    David Hernandez

  3. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Kailash C. Misra

  4. Department of Mathematics, Catholic University of America, Washington D.C., WA, USA

    Prasad Senesi

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Hernandez, D., Leclerc, B. (2021). Quantum Affine Algebras and Cluster Algebras. In: Greenstein, J., Hernandez, D., Misra, K.C., Senesi, P. (eds) Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification. Progress in Mathematics, vol 337. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-63849-8_2

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