Thursday 14 Dec 2017: Representations of W-algebras and reduced enveloping algebras for modular \gl(m|n)
Dr Simon Goodwin - University of Birmingham
Finite dimensional representations of simple Lie algebras over the complex numbers have been well understood for a long time. However, the representation theory of Lie algebras of simple algebraic groups over field of positive characteristic is less well understood. We'll start by surveying some of the known theory of modular representations of simple Lie algebras including reduced enveloping algebras and the Kac--Weisfeiler conjecture, which is now a theorem of Premet. This leads on to the definition of the minimal dimensional modules for reduced enveloping algebras, and the problem of determining them. In the case of general linear Lie algebras, we'll present joint work with Topley giving a classification of these modules, and then explain that these methods can also be extended to general linear Lie superalgebras.