Good grading polytopes

Mathematics – Quantum Algebra

Scientific paper

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27 pages

Scientific paper

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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