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) Leonardo PATIMO - Albert-Ludwigs-Universität Freiburg,
Titre Dyck partitions and the intersection cohomology of Schubert varieties
Horaire14:00 à 15:00
RésumeThe cohomology of Schubert varieties is a very classical object of study, and we can understand it thoroughly thanks to a crucial tool: its Schubert basis. From a representation theory point of view, it is often more natural to look instead at the intersection cohomology of this varieties. However, understanding the intersection cohomology is in general a much more difficult task. In this talk we will focus on Schubert varieties inside Grassmannians, which have many special features among Schubert varieties. The related Kazhdan-Lusztig polynomials, in fact, can be realized combinatorially: we can compute them by counting certain Dyck partitions. In this talk we will explain how, by ``lifting'' the rich combinatorics of this Dyck partitions to the category of singular Soergel bimodules we are able to extend the Schubert basis to a basis of the intersection cohomology.
Sallesalle 2015, 2em étage,
AdresseSophie Germain