# Séminaires : Séminaire Groupes, Représentations et Géométrie

 Equipe(s) : gr, Responsables : A. Brochier, O. Brunat, J.-Y. Charbonnel, O. Dudas, E. Letellier, D. Juteau, M. Varagnolo, E. Vasserot Email des responsables : Adrien Brochier , Olivier Brunat , Jean-Yves Charbonnel , Olivier Dudas , Emmanuel Letellier , Daniel Juteau , Michela Varagnolo , Eric Vasserot Salle : salle 2015, 2em étage, Adresse : Sophie Germain Description

 Orateur(s) Claude EICHER - ETHZ, Titre Relaxed highest weight representations from D-modules on the Kashiwara flag scheme Date 21/10/2016 Horaire 10:30 à 11:30 Résume The relaxed highest weight representations introduced by Feigin, Semikhatov and Tipunin are a special class of representations of the Lie algebra affine $\hat{\mathfrak{sl}_2}$, which do not have a highest (or lowest) weight. We formulate a generalization of this notion for an arbitrary affine Kac-Moody algebra $\mathfrak{g}$. We then realize induced $\mathfrak{g}$-modules of this type and their duals as global sections of twisted $\mathcal{D}$-modules on the Kashiwara flag scheme associated to $\mathfrak{g}$. The $\mathcal{D}$-modules that appear in our construction are direct images from subschemes given by the intersection of finite dimensional Schubert cells with their translate by a simple reflection. Besides the twist, they depend on a complex number describing the monodromy of the local systems we construct on these intersections. These results describe for the first time explicit non-highest weight $\mathfrak{g}$-modules as global sections on the Kashiwara flag scheme and extend several results of Kashiwara-Tanisaki to the case of relaxed highest weight representations. This is based on the preprint \href{https://arxiv.org/abs/1607.06342}{arxiv1607.06342} [math.RT]. Salle salle 2015, 2em étage, Adresse Sophie Germain