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 : à distance / remote
Adresse :IHP

Depuis le 23 mars 2020, le séminaire se tient 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) Sachin GAUTAM - Columbia, New York,
Titre Tensor isomorphism between Yangians and quantum loop algebras
Horaire14:00 à 15:00
RésumeThe Yangian and the quantum loop algebra of a simple Lie algebra arise naturally in the study of the rational and trigonometric solutions of the Yang--Baxter equation, respectively. The aim of this talk is to establish an explicit relation between these Hopf algebras. More precisely, we will show that a certain subcategory of finite--dimensional representations of the Yangian is isomorphic, as a tensor category, to the category of finite--dimensional representations of the quantum loop algebra. The isomorphism between these two categories is governed by the monodromy of an abelian difference equation. Moreover, the twist relating the tensor products is a solution of an abelian version of the qKZ equations of Frenkel and Reshetikhin. These results are part of an ongoing project, joint with V. Toledano Laredo.
Salleà distance / remote