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Proceedings of the London Mathematical Society Advance Access originally published online on November 27, 2006
Proceedings of the London Mathematical Society 2007 94(1):155-180; doi:10.1112/plms/pdl009
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© 2006 London Mathematical Society

Good grading polytopes

Jonathan Brundan1 and Simon M. Goodwin2,*

1 Department of Mathematics
University of Oregon
Eugene, OR 97403
USA
brundan{at}darkwing.uoregon.edu
2 Institut for Matematiske Fag
Aarhus Universitet
DK-8000 Aarhus C
Denmark

Received 13 October 2005. Revision received 29 March 2006.

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

* Current address: School of Mathematics, University of Birmingham, Birmingham, B15 2TT, United Kingdom, goodwin{at}maths.bham.ac.uk.


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Home page
 Int Math Res NoticesHome page
J. Brundan, S. M. Goodwin, and A. Kleshchev
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Int Math Res Notices, January 1, 2008; 2008(rnn051): rnn051 - 53.
[Abstract] [PDF]


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