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Good grading polytopes

Jonathan Brundan·Simon M. Goodwin
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Abstract

Let g be a finite dimensional semisimple Lie algebra over C and e be 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.

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Jonathan Brundan, Simon M. Goodwin. 2005-10-10. Good grading polytopes. https://arxiv.org/abs/math/0510205

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