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) Ryo FUJITA - Université de Paris,
Titre Twisted Auslander-Reiten quivers, quantum Cartan matrix and representation theory of quantum affine algebras
Horaire14:00 à 15:00
RésumeFor a complex simple Lie algebra $g$, its quantum Cartan matrix plays an important role in the representation theory of the quantum affine algebra of $g$. When $g$ is of type ADE, Hernandez-Leclerc (2015) related its quantum Cartan matrix with the representation theory of Dynkin quivers and hence with the combinatorics of adapted words in the Weyl group of the corresponding ADE type. In this talk, we introduce the notion of Q-data, which can be regarded as a combinatorial generalization of a Dynkin quiver with height function, and its twisted Auslander-Reiten quiver. Using them, we relate the quantum Cartan matrix of type BCFG with the combinatorics of twisted adapted words in the Weyl group of the corresponding unfolded ADE type introduced by Oh-Suh (2019). Also, we see their relation to the representation theory of quantum affine algebras. For example, we present a (partially conjectural) unified expression of the denominators of R-matrices between the Kirillov-Reshetikhin modules in terms of the quantum Cartan matrices. This is a joint work with Se-jin Oh.
Salleà distance / remote