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On changing highest weight theories for finite W-algebras

Authors
  • Brown, Jonathan S.
  • Goodwin, Simon M.
Type
Preprint
Publication Date
May 17, 2011
Submission Date
May 17, 2011
Source
arXiv
License
Yellow
External links

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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