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 : 001
Adresse :IHP


Orateur(s) Matheus BRITO - Paraná,
Titre Tensor products of prime representations of quantum affine $sl_{n+1}$ (projet ERC QAffine)
Horaire14:00 à 15:00
RésumeWe 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