%0 Journal Article
%T On changing highest weight theories for finite W-algebras
%A Jonathan S. Brown
%A Simon M. Goodwin
%J Mathematics
%D 2011
%I arXiv
%X A highest weight theory for a finite W-algebra U(g,e) was developed in [BGK]. This leads to a strategy for classifying the irreducible finite dimensional U(g,e)-modules. The highest weight theory depends on the choice of a parabolic subalgebra of g leading to different parameterizations of the finite dimensional irreducible U(g,e)-modules. We explain how to construct an isomorphism preserving bijection between the parameterizing sets for different choices of parabolic subalgebra when g is of type A, or when g is of types C or D and e is an even multiplicity nilpotent element
%U http://arxiv.org/abs/1105.3308v1