Abstract

On induced completely prime primitive ideals in enveloping algebras of classical Lie algebras

Abstract: The classification of completely prime primitive ideals in enveloping algebras of simple complex Lie algebras is long-standing classical problem in representation. Although the classification of all primitive ideals as a set was established in the 1980s the problem for completely prime primitive ideals has proved much more challenging. In this talk we will cover recent work in which we show that an important class of completely prime primitive ideals, which we refer to as Losev—Premet ideals, can be understood through a process of parabolic induction in the case of simple Lie algebras of classical type. We’ll explain how this can be reduced to problem about 1-dimensional representations of finite W-algebra. At the end of the talk, we’ll explain a modular analogue of these results about minimal dimensional representations of reduced enveloping algebras.