Paris Diderot Sorbonne Université CNRS

Groupes, Représentations et Géométrie

On equivariantly irreducible modular representations of a semisimple Lie algebra

Ivan Losev - MIT

vendredi 22 février 2019 à 14:00
Sophie Germain en salle 1016 à 14 h 00

8 place Aurélie Nemours, 75013 Paris

In this talk I will discuss the representation theory of semisimple Lie algebras g in very large positive characteristic p. To an irreducible representation one can assign its p-character, essentially an element of 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 repsentation theory of g in characteristic p as well as known results.

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