Modular finite W-algebras and their one dimensional representations

Lewis Topley (Kent)

Frank Adams 1,

I will report on a joint work with Simon Goodwin: we prove a conjecture of Premet which states that the modules of minimal dimension for reduced enveloping algebras of general linear algebras are all parabolically induced. Our method is to study ​finite W-algebras in characteristic \(p\) and it reveals, amongst other things, that the conjecture is a modular analogue of a classical result of Moeglin stating that completely prime primitive ideals in enveloping algebras of complex general linear algebras are all parabolically induced.

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