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H 1 Correspondence functors

Auteurs : Bouc, Serge (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this joint work with Jacques Thévenaz, we develop the representation theory of finite sets and correspondences : let kC the category of finite sets, in which morphisms are k-linear combinations of correspondences (where k is a given commutative ring), and let Fk be the category of correspondence functors (over k), i.e. the category of k-linear functors from kC to k-modules. This category Fk is an abelian k-linear category. In such a framework, it is of crucial importance to describe the algebra of essential endomorphisms of a given object. This is what we achieved in a previous work on the algebra of essential relations on a finite set, describing in particular its simple modules. This description leads to a parametrization of the simple functors on kC by triples (E;R;V) consisting of a finite set E, a partial order relation R on E, and a simple k-linear representation V of the automorphism group of (E;R).

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      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 23/09/14
      Date de captation : 22/09/14
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 01:00:25
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-09-22_Bouc.mp4

    Informations sur la rencontre

    Nom de la rencontre : Algebraic and finite groups, geometry and representations. 50 years of Chevalley seminar / Groupes algébriques, groupes finis, géométries, représentations : 50 ans de séminaire Chevalley.
    Organisateurs de la rencontre : Brunat, Olivier ; Cabanes, Marc ; Kessar, Radha
    Dates : 22/09/14 - 26/09/14
    Année de la rencontre : 2014

    Citation Data

    DOI : 10.24350/CIRM.V.18601203
    Cite this video as: Bouc, Serge (2014). Correspondence functors. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18601203
    URI : http://dx.doi.org/10.24350/CIRM.V.18601203


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