AbstractWe use the theory of finite W-algebras associated to nilpotent orbits in the Lie algebra $\mathfrak {g} = \mathfrak {gl}_N({\mathbb C})$ to give another proof of Mœglin’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.
MULTIPLICITY-FREE PRIMITIVE IDEALS ASSOCIATED WITH RIGID NILPOTENT ORBITS