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) Tsukasa ISHIBASHI - Tokyo,
Titre Cluster realizations of Coxeter groups and their relations with higher Teichmuller spaces (Projet ERC QAffine)
Horaire14:00 à 15:00
RésumeFor a Coxeter group $W$ satisfying some mild conditions, we construct a family of seeds such that the corresponding cluster modular group contains $W$ as a subgroup. It is a generalization of the construction for type $A_n$ given by Inoue-Lam-Pylyavskyy. Moreover, we show that one of our seed for type $A_n$ is mutation- equivalent to the $SL_{n+1}$-higher Teichmuller seed for the punctured disk with even number of marked points on its boundary. In particular $W(A_n)$ acts on the moduli space of decorated (twisted) local systems. We show that this action coincides with that given by Goncharov-Shen, which is also a cluster action. This talk is based on a joint work with Rei Inoue.