关于有限W-代数的变最高权理论
On changing highest weight theories for finite W-algebras
摘要：
[BGK]给出了有限W-代数U（g，e）的一个最高权理论.这导致了一个战略分类的不可约有限维U（g，e）-模。最高权理论依赖于g的抛物子代数的选择，从而导致有限维不可约U（g，e）-模的不同参数化。当g为A型，或g为C型或D型，e为偶重幂零元幂零元时，我们给出了抛物子代数的不同选择的参数化集之间的保同构双射的构造
英文摘要：
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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