On changing highest weight theories for finite W-algebras
Representation Theory
2011-05-18 v1
Abstract
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
Keywords
Cite
@article{arxiv.1105.3308,
title = {On changing highest weight theories for finite W-algebras},
author = {Jonathan S. Brown and Simon M. Goodwin},
journal= {arXiv preprint arXiv:1105.3308},
year = {2011}
}
Comments
25 pages