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) Lauren WILLIAMS - Berkeley,
Titre Quiver representations and generalized minors
Horaire14:00 à 15:00
RésumeThe representation theories of both quivers and of Kac-Moody groups are described by certain ternary classifications. On one hand, indecomposable quiver representations are classified as either preprojective, preinjective, or regular according to the action of the Auslander-Reiten translation. On the other, irreducible representations of affine Kac-Moody groups are classified as highest-weight, lowest-weight, or level zero according to their central character (similarly for non-affine types, though the term ``level zero'' is less apt). In both classifications the first two classes are well understood and dual to each other in a suitable sense, while the third is much more mysterious. The theme of the talk is that these two classifications are in fact directly related to one another. We formulate a general conjecture to this effect, which we prove in affine type A and finitely many other types. The conjecture is couched in terms of cluster algebras -- on one hand these are repositories for certain generating functions (called cluster characters) associated to quiver representations, and on the other they are coordinate rings of certain subvarieties of Kac-Moody groups. The conjecture states that the cluster character of a rigid indecomposable quiver representation is a generalized minor of a specific Kac-Moody representation, and that this relationship intertwines the classifications described above. This is joint work with Dylan Rupel and Salvatore Stella.
Salleà distance / remote