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 :

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) Elie CASBI - Bonn,
Titre Equivariant multiplicities of simply-laced type flag minors
Horaire14:00 à 15:00
RésumeThe study of remarkable bases of (quantum) coordinate rings has been an area of intensive research since the early 90's. For instance, the multiplicative properties of these bases (in particular the dual canonical basis) was one of the main motivations for the introduction of cluster algebras by Fomin and Zelevinsky around 2000. In recent work, Baumann-Kamnitzer-Knutson introduced an algebra morphism  $\overline{D}$ from the coordinate algebra $\mathbb{C}[N]$ of a maximal unipotent subgroup $N$ to the function field of a maximal torus. It is related to the geometry of Mirkovic-Vilonen cycles via the notion of equivariant multiplicity. This morphism turns out to be useful for comparing good bases of the coordinate algebra $\mathbb{C}[N]$. We will focus on comparing the values taken by $\overline{D}$ on several distinguished elements of the Mirkovic-Vilonen basis and the dual canonical basis. For the latter one, we will use Kang-Kashiwara-Kim-Oh's monoidal categorification of the cluster structure of the cluster structure of $\mathbb{C}[N]$ via quiver Hecke algebras as well as recent results by Kashiwara-Kim. This will lead us to an explicit description of the images under $\overline{D}$ of the flag minors of $\mathbb{C}[N]$ as well as remarkable identities between them.
SalleInfo sur https://researchseminars.org/seminar/paris-algebra-seminar