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) D. JORDAN - Université de Sheffield,
Titre Quantum Springer-Hotta-Kashiwara modules via Schur-Weyl duality
Horaire14:00 à 15:00
RésumeSpringer theory constructs representations of the Weyl group $W$ of a reductive group $G$ from the geometry of the Springer resolution of the nilpotent cone in $g=Lie(G)$. Hotta and Kashiwara translated Springer's construction to the language of $D$-modules, and when $G=GL_N$ results of Calaque, Enriquez, and Etingof highlighted a certain compatiblity of this $D$-module with classical Schur-Weyl duality. In the geometric theory of quantum groups, we consider instead an algebra $D_q(G)$, of ``$q$-difference`` operators on $G$. I'll report on joint work in progress with Monica Vazirani, where we construct $q$-deformations of Hotta and Kashiwara's $D(G)$-modules to the algebra $D_q(G)$, and we study these using a ''genus one`` quantum Schur-Weyl duality.''
Sallesalle 2015, 2em étage,
AdresseSophie Germain