Yangians and representations of the general linear Lie algebra in positive characteristic

In this talk I will discuss the representation theory of the general linear Lie algebra over a field of positive characteristic. The irreducible representations factor through certain quotients of the enveloping algebra, known as reduced enveloping algebras. It turns out that these reduced enveloping algebras may be described completely by examining a finite collection of such algebras, labelled by the conjugacy classes of nilpotent matrices of rank n. Premet has shown that each of these reduced enveloping algebras is actually Morita equivalent to an algebra known as a restricted finite W-algebra. The main result of this talk is a joint work with Simon Goodwin, in which we show that these restricted finite W-algebras can be described explicitly as certain subquotients of a Yangian.