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
Description

Orateur(s) Paul-James WHITE - Institut Mathématique de Jussieu,
Titre Monodromy of the Gaudin system in type A
Date11/03/2016
Horaire10:30 à 11:30
RésumeThe Gaudin Hamiltonians are a set of commuting operators depending on a set of complex parameters. These operators act on tensor products of irreducible representations of the general linear Lie algebra. The problem of understanding the spectrum of these operators has attracted significant attention recently. We describe the monodromy of the spectrum of the Hamiltonians for real values of the parameters and show that it is related to the tensor structure on the category of crystals for the general linear Lie algebra. In a special case, the spectrum of the Hamiltonians is isomorphic to the spectrum of the centre of the rational Cherednik algebra in type A. Using the geometry of the centre of the rational Cherednik algebra, Bonnafe and Rouquier have given a conjectural construction of Kazhdan-Lusztig cells (for all complex reflection groups). The monodromy action we describe recovers the Kazhdan-Lusztig cells of the symmetric group.
Sallesalle 2015, 2em étage,
AdresseSophie Germain
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