Good grading polytopes

By Jonathan Brundan, Simon M. Goodwin. 2005

79 citations recorded by the source corpus.

Let 𝔤 be a finite‐dimensional semisimple Lie algebra over ℂ and e ∈ 𝔤 a nilpotent element. Elashvili and Kac have recently classified all good ℤ‐gradings for e. We instead consider good ℝ‐gradings, which are naturally parameterized by an open convex polytope in a Euclidean space arising from the reductive part of the centralizer of e in 𝔤. As an application, we prove that the isomorphism type of the finite W‐algebra attached to a good ℝ‐grading for e is independent of the particular choice of good grading.

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

View Paper: https://www.semanticscholar.org/paper/09a9df329eb22e1a1cbc57206393e42788bee2c9

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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

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2. V. Ginzburg
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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): “Moreover, Brundan and Goodwin proved in [ BrG ] that U (g ,e ) does not depend on the choice ofh� up to an isomorphism of algebras.”