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 - Kyoto,
Titre Isomorphims among quantum Grothendieck rings and propagation of positivity
Horaire14:00 à 15:00
RésumeFor a complex simple Lie algebra $\mathfrak{g}$, finite-dimensional representations of its quantum loop algebra form an interesting monoidal abelian category, which has been studied from various perspectives. Related to the fundamental problem of determining the characters of irreducible representations, we consider its quantum Grothendieck ring, a 1-parameter deformation of the usual Grothendieck ring. When $\mathfrak{g}$ is of simply-laced type, Nakajima and Varagnolo-Vasserot proved that it enjoys some positivity properties based on the geometry of quiver varieties. In this talk, we show that the same positivities hold also for non-simply-laced type by establishing an isomorphism between the quantum Grothendieck ring of non-simply-laced type and that of ''unfolded'' simply-laced type. In addition, we find that an analog of Kazhdan-Lusztig conjecture holds for several new cases in non-simply-laced type. This is a joint work with David Hernandez, Se-jin Oh, and Hironori Oya.
Salleà distance / remote