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 <adrien.brochier@imj-prg.fr>, Olivier Brunat <olivier.brunat@imj-prg.fr>, Jean-Yves Charbonnel <jean-yves.charbonnel@imj-prg.fr>, Olivier Dudas <olivier.dudas@imj-prg.fr>, Emmanuel Letellier <emmanuel.letellier@imj-prg.fr>, Daniel Juteau <daniel.juteau@imj-prg.fr>, Michela Varagnolo <varagnol@math.u-cergy.fr>, Eric Vasserot <eric.vasserot@imj-prg.fr>
Salle : salle 2015, 2em étage,
Adresse :Sophie Germain

Orateur(s) Claude EICHER - ETHZ,
Titre Relaxed highest weight representations from D-modules on the Kashiwara flag scheme
Horaire10:30 à 11:30
RésumeThe 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].
Sallesalle 2015, 2em étage,
AdresseSophie Germain