与截断电流李代数相关的有限w代数

Pub Date : 2022-06-28 DOI:10.3336/gm.57.1.02

Xiao He

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引用次数: 0

摘要

研究了与截断电流李代数相关的有限w代数。我们证明了有限w -代数在半简单情况下的一些性质在截断电流情况下仍然成立。特别地，Kostant定理和Skryabin等价在我们的例子中成立。作为应用，我们给出了截断电流李代数在\(s\ell_2\)情况下的简单Whittaker模的分类。

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Finite W-algebras associated to truncated current Lie algebras

Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \(s\ell_2\) case.

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