Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :Zoom ou IHP Salle 01

Le séminaire est prévu en présence à l'IHP et à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


Orateur(s) Edward FRENKEL - Université de Berkeley et I.M.J.,
Titre Opers with irregular singularity and shift of argument subalgebra
Horaire14:30 à 15:30
RésumeThe universal enveloping algebra of any simple Lie algebra g contains a family of commutative subalgebras, called the quantum shift of argument subalgebras. Recently B. Feigin, L. Rybnikov and myself have proved that generically their action on finite-dimensional modules is diagonalizable and their joint spectra are in bijection with differential geometric objects on the projective line called ``opers''. They have regular singularity at one point, irregular singularity at another point and are monodromy free. Interestingly, they are associated not to G, but to the Langlands dual group of G. In addition, we have shown that the quantum shift of argument subalgebra corresponding to a regular nilpotent element of g has a cyclic vector in any irreducible finite-dimensional g-module. As a byproduct, we obtain the structure of a Gorenstein ring on any such module. I will talk about these results and explain their connection to the geometric Langlands correspondence.
SalleZoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar
AdresseZoom ou IHP Salle 01