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 : Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :
Description

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) Duncan Laurie - Oxford,
Titre Quantum toroidal algebras: braid group actions, automorphisms, and representation theory
Date02/10/2023
Horaire14:00 à 15:00
Diffusion
Résume

Quantum toroidal algebras Uq(g_tor) occur as the Drinfeld quantum affinizations of quantum affine algebras. In particular; they contain (and are generated by) a horizontal and vertical copy of the affine quantum group. In type A, Miki obtained an automorphism of Uq(g_tor) exchanging these subalgebras, which has since played a crucial role in the investigation of its structure and representation theory.

In this talk; we shall construct an action of the extended double affine braid group B on the quantum toroidal algebra in all untwisted types. In the simply laced cases, using this action and certain involutions of B we obtain automorphisms and anti-automorphisms of Uq(g_tor) which exchange the horizontal and vertical subalgebras, thus generalising the results of Miki. We shall then discuss potential extensions of these results, and applications to the representation theory of quantum toroidal algebras.

This talk will take place in hybrid mode at the Institut Henri Poincaré.

SalleInfo sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse
© IMJ-PRG