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) Gleb KOSHEVOY - ,
Titre Products of Kirillov-Reshetikhin modules and maximal green sequences
Date31/03/2025
Horaire14:00 à 15:00
Diffusion
Résume

We show that a qq-character of a Kirillov-Reshetikhin module (KR modules) for untwisted quantum affine algebras of simply laced types $A_n^{(1)}$​,  $D_n^{(1)}$​,  $E_6^{(1)}$​,  $E_7^{(1)}$​,  $E_8^{(1)}$​, might be obtained from a specific cluster variable of a seed obtained by applying a maximal green sequence to the initial (infinite) quiver of the Hernandez-Leclerc cluster algebra. For a collection of KR-modules with nested supports, we show an explicit construction of a cluster seed, which has cluster variables corresponding to the qq-characters of KR-modules of such a collection. We prove that the product of KR-modules of such a collection is a simple module. We also have an explicit construction of cluster seeds with cluster variables corresponding to qq-characters of KR-modules of some non-nested collections. We make a conjecture that tensor products of KR-modules for such non-nested collections are simple. If time permits, I explain that the cluster Donaldson-Thomas transformations for double Bruhat cells for ADE types can be computed using qq-characters of KR-modules, and new algorithm to compute qq-characters KR-modules. The talk is based on joint work with Y.Kanakubo and T.Nakashima.

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