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) Ivan LOSEV - MIT,
Titre On equivariantly irreducible modular representations of a semisimple Lie algebra
Horaire14:00 à 15:00
RésumeIn this talk I will discuss the representation theory of semisimple Lie algebras $\mathfrak{g}$ in very large positive characteristic $p$. To an irreducible representation one can assign its $p$-character, essentially an element of $\mathfrak{g}$. The most interesting case is when it is nilpotent. While a lot is known about the irreducible representations and their classes in $K_{0}$, there is no combinatorial classification of the irreducibles and no explicit dimension formulas for an arbitrary nilpotent $p$-character. A basic case creating difficulties is when the $p$-character is distinguished, i.e., is not contained in a proper Levi subalgebra. I will review some basics of the representation theory of $\mathfrak{g}$ in characteristic $p$ as well as known results. Then I will discuss my current work with Bezrukavnikov, where we get a combinatorial classification and Kazhdan-Lusztig type formulas for $K_0$-classes of equivariantly irreducible modules with distinguished $p$-character, where the equivariance is for the action of the centralizer.
Sallesalle 2015, 2em étage,
AdresseSophie Germain