Primitive ideals, non-restricted representations and finite W-algebras

By A. Premet. 2006

48 citations recorded by the source corpus.

We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish a connection between primitive ideals of U(g) attached to the nilpotent orbit containing e and finite-dimensional representations of the reduced enveloping algebra assiciated with e over an algebraically closed field of finite characteristic.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ad0f1eaf8f145bc7f9e8345055b53cd6a0e6dbf1

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In Algebra and Number Theory

1. I. Losev
2. T. Arakawa
3. V. Ginzburg
4. A. Premet
5. I. Gordon
6. Ben Webster

In Geometry and Topology

1. I. Losev
2. V. Ginzburg
3. T. Arakawa
4. A. Premet
5. I. Gordon
6. Ben Webster

In Mathematical Physics

1. I. Losev
2. V. Ginzburg
3. T. Arakawa
4. A. Premet
5. I. Gordon
6. Ben Webster

Citations in the corpus

• Quantized symplectic actions and W -algebras (2007, background): “From assertion (viii) of Theorem 1.2.2 we deduce that W has a nontrivial finite-dimensional irreducible module, say V (this result was obtained previously by Premet, [ Pr3 ]).”