Moeglin's theorem and Goldie rank polynomials in Cartan type A

TL;DR

This paper provides a new proof of Moeglin's theorem on primitive ideals in the enveloping algebra of gl_N(C) using finite W-algebras and offers new insights into Joseph's Goldie rank polynomials in type A.

Contribution

It introduces an alternative proof of Moeglin's theorem via finite W-algebras and presents novel observations on Goldie rank polynomials in Cartan type A.

Findings

New proof of Moeglin's theorem using finite W-algebras

Additional insights into Joseph's Goldie rank polynomials in type A

Enhanced understanding of primitive ideals in gl_N(C)

Abstract

We use the theory of finite W-algebras associated to nilpotent orbits in the Lie algebra g = gl_N(C) to give another proof of Moeglin's theorem about completely prime primitive ideals in the enveloping algebra U(g). We also make some new observations about Joseph's Goldie rank polynomials in Cartan type A.