# 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 , Olivier Brunat , Jean-Yves Charbonnel , Olivier Dudas , Emmanuel Letellier , Daniel Juteau , Michela Varagnolo , Eric Vasserot Salle : salle 2015, 2em étage, Adresse : Sophie Germain Description

 Orateur(s) Ivan LOSEV - MIT, Titre On equivariantly irreducible modular representations of a semisimple Lie algebra Date 22/02/2019 Horaire 14:00 à 15:00 Diffusion Résume In 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. Salle salle 2015, 2em étage, Adresse Sophie Germain