Mathematics – Representation Theory
Scientific paper
2010-09-16
Mathematics
Representation Theory
This version is accepted for publication (many typos and minor errors are corrected, several new remarks, etc)
Scientific paper
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.
No associations
LandOfFree
Enveloping algebras of Slodowy slices and Goldie rank does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Enveloping algebras of Slodowy slices and Goldie rank, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Enveloping algebras of Slodowy slices and Goldie rank will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-28040