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- W4300789712 abstract "It is known that any primitive ideal I of U(g) whose associated variety contains a nilpotent element e in its open G-orbit admits a finite generalised Gelfand-Graev model which is a finite dimensional irreducible module over the finite W-algebra U(g,e). We prove that if V is such a model for I, then the Goldie rank of the primitive quotient U(g)/I always divides the dimension of V. For g=sl(n), we use a result of Joseph to show that the Goldie rank of U(g)/I equals the dimension of V and we show that the equality conntinues to hold outside type A provided that the Goldie field of U(g)/I is isomorphic to a Weyl skew-field. As an application of this result, we disprove Joseph's conjecture on the structure of the Goldie fields of primitive quotients of U(g) formulated in the mid-70s." @default.
- W4300789712 created "2022-10-04" @default.
- W4300789712 creator A5075632220 @default.
- W4300789712 date "2010-09-16" @default.
- W4300789712 modified "2023-10-18" @default.
- W4300789712 title "Enveloping algebras of Slodowy slices and Goldie rank" @default.
- W4300789712 doi "https://doi.org/10.48550/arxiv.1009.3229" @default.
- W4300789712 hasPublicationYear "2010" @default.
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