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H 1 Hamiltonian reduction for affine Grassmannian slices

Auteurs : Kamnitzer, Joel (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Given a representation V of a reductive group G, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb branch algebra. Important cases of these Coulomb branches are (generalized) affine Grassmannian slices, and their quantizations are truncated shifted Yangians.
    Motivated by the geometric Satake correspondence and the theory of symplectic duality/3d mirror symmetry, we expect a categorical g-action on modules for these truncated shifted Yangians. I will explain three results in this direction. First, we have an indirect realization of this action, using equivalences with KLRW-modules. Second, we have a geometric relation between these generalized slices by Hamiltonian reduction. Finally, we have an algebraic version of this Hamiltonian reduction which we are able to relate to the first realization.

    Keywords : representation theory; affine Grassmannian; truncated shifted Yangians; Coulomb branches

    Codes MSC :


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


      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 11/01/2021
      Date de captation : 14/12/2020
      Collection : Algebra ; Lie Theory and Generalizations
      Sous collection : Research talks
      arXiv category : Representation Theory ; Algebraic Geometry ; Quantum Algebra ; Rings and Algebras
      Domaine : Algebra ; Lie Theory and Generalizations
      Durée : 01:02:54
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-12-14_Kamnitzer.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.19693203
    Cite this video as: Kamnitzer, Joel (2020). Hamiltonian reduction for affine Grassmannian slices.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.19693203
    URI : http://dx.doi.org/10.24350/CIRM.V.19693203


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