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

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

2010-09-20

arxiv.org/abs/1009.3869v2

Mathematics

Representation Theory

38 Pages; made some minor corrections

Scientific paper

We consider finite W-algebras U(g,e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g,e)-modules with integral central character in terms of the highest weight theory for finite W-algebras. As a corollary, we obtain a parametrization of primitive ideals of U(g) with associated variety the closure of the adjoint orbit of e and integral central character.

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