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Good grading polytopes
Author(s) -
Brundan Jonathan,
Goodwin Simon M.
Publication year - 2007
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdl009
Subject(s) - mathematics , polytope , centralizer and normalizer , euclidean space , parameterized complexity , algebra over a field , lie algebra , pure mathematics , combinatorics
Let be a finite‐dimensional semisimple Lie algebra over ℂ and e ∈ 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 . 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.