English

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

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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}
}

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25 pages