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H 1 Shifted quantum affine algebras, monoidal categorication and Langlands duality

Auteurs : Hernandez, David (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In the framework of the study of K-theoretical Coulomb branches, Finkelberg-Tsymbaliuk introduced remarkable new algebras, the shifted quantum affine algebras an their truncations, in the spirit of the shifted Yangians of Brundan-Kleshev, Braverman-Finkelberg Nakajima, Kamnitzer-Webster-Weekes-Yacobi... We discuss the following points in representation theory of (truncated) shifted quantum affine algebras that we relate to representations of Borel quantum affine algebras by induction and restriction functors. We establish that the Grothendieck ring of the category of finite-dimensional representations has a natural cluster algebra structure. We propose a conjectural parametrization of simple modules of a non simply-laced truncation in terms of the Langlands dual quantum affine Lie algebra. We have several evidences, including a general result for simple finite-dimensional representations proved by using the Baxter polynomiality of quantum integrable models.

    Keywords : Shifted quantum affine algebras and truncations; quantum affine Borel algebras; category O; fusion product; categorication of cluster algebras; Baxter polynomials; Langlands interpolation

    Codes MSC :
    17B10 - Representations of Lie algebras, algebraic theory
    17B37 - Quantum groups and related deformations
    82B23 - Exactly solvable models; Bethe ansatz
    13F60 - Cluster algebras


    Ressources complémentaires :
    https://www.cirm-math.fr/RepOrga/2221/Slides/Hernandez-slides.pdf


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 11/01/2021
      Date de captation : 14/12/2020
      Collection : Research talks ; Algebra ; Lie Theory and Generalizations ; Mathematical Physics
      Durée : 00:52:58
      Domaine : Algebra ; Mathematical Physics ; Lie Theory and Generalizations
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-12-14_Hernandez.mp4

    Informations sur la Rencontre Virtuelle

    Nom de la rencontre : Quantum Groups and Cohomology Theory of Quiver and Flag Varieties / Groupes quantiques et théories cohomologiques des variétés de drapeaux et variétés carquois
    Organisateurs de la rencontre : Leclerc, Bernard ; Mihalcea, Leonardo ; Perrin, Nicolas ; Varagnolo, Michela
    Dates : 14/12/2020 - 18/12/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2221.html

    Citation Data

    DOI : 10.24350/CIRM.V.19693103
    Cite this video as: Hernandez, David (2020). Shifted quantum affine algebras, monoidal categorication and Langlands duality.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19693103
    URI : http://dx.doi.org/10.24350/CIRM.V.19693103


    Voir aussi

    Bibliographie

    1. HERNANDEZ, David. Representations of shifted quantum affine algebras. arXiv preprint arXiv:2010.06996, 2020. - https://arxiv.org/abs/2010.06996

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