Finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent orbits in classical Lie algebras

• Published in: Mathematische Zeitschrift Vol. 273; no. 1-2; pp. 123 - 160
• Main Authors: Brown, Jonathan S., Goodwin, Simon M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-02-2013
• Subjects: Mathematics; Mathematics and Statistics; 81R05; 17B10
• ISSN: 0025-5874; 1432-1823
• DOI: 10.1007/s00209-012-0998-8

We consider finite
W
-algebras
associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible
-modules with integral central character in terms of the highest weight theory from Brundan et al. (Int. Math. Res. Notices 15, art. ID rnn051,
2008
). As a corollary, we obtain a parametrization of primitive ideals of
with associated variety the closure of the adjoint orbit of
e
and integral central character.