SPEAKER: Ivan Losev

TITLE: Goldie ranks via finite W-algebras

ABSTRACT: The study of primitive ideals in enveloping algebras of semisimple Lie algebras is a classical topic in Lie representation theory. One of the remaining famous open problems there is to calculate Goldie ranks of primitive ideals. This problems was extensively studied by Joseph in the 80's. Recently, there was a renewed interest to this problem due to its relation to finite W-algebras (Premet, Brundan and myself): often it happens that the Goldie ranks are equal to dimensions of irreducible modules over W-algebras. The goal of this talk is to outline my recent results in this direction. Unfortunately, due to the lack of time the explanation on W-algebras will be reduced to the necessary minimum.