# 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 , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : à distance / remote Adresse : IHP Description 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) Matheus BRITO - Paraná, Titre Tensor products of prime representations of quantum affine $sl_{n+1}$ (projet ERC QAffine) Date 05/12/2016 Horaire 14:00 à 15:00 Diffusion Résume We study the family of prime representations of quantum affine $sl_{n+1}$ introduced in the work of Hernandez and Leclerc. These are defined by using an $A_n$-quiver; in the case of the sink-source quiver and the monotonic quiver they proved that the associated subcategory of finite–dimensional representations of the quantum affine algebra was a monoidal categorification of a cluster algebra with the prime representations corresponding to cluster variables. In this talk we shall work with an arbitrary quiver and give a necessary and sufficient condition in terms of Drinfeld polynomials for a tensor product of prime representations to be irreducible. We also state precisely the “exchange relations” in the case when a tensor product is reducible; in other words we describe the Jordan–Holder series of the tensor product. As a consequence of our results we write an explicit formula for the character of a prime representation as an alternating linear combination of characters of the local Weyl modules for quantum affine algebras. The talk is based on a joint work with Vyjayanthi Chari Salle à distance / remote Adresse IHP