A characteristic variety for the primitive spectrum of a semisimple lie algebra
A characteristic variety for the primitive spectrum of a semisimple lie algebra
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半单李代数本原谱的特征簇
DOI：
10.1007/bfb0087917
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发表时间：
1977
期刊：
影响因子：
--
通讯作者：
A. Joseph
中科院分区：
文献类型：
--
作者：
A. Joseph
M.Duflo[5]最近证明了特征为零域上的分裂半单李代数的本原谱就是Verma模的单商的零化子的集合。在此基础上，定义了包络代数中双边理想的一个特征簇，并用它给出了具有相同中心特征的本原理想纤维上Duflo序原理的一个新的初等证明。本文的主要新结果(定理15)证明了Weyl群被分解成不相交的子集(胞元)，使得给定胞腔中的每个点定义相同的理想(通过Duflo定理)。人们推测，不同的细胞对应着不同的理想，这一结果将对本原谱进行分类。
M. Duflo [5] has recently shown that the primitive spectrum of a split semisimple Lie algebra over a field of characteristic zero is just the set of annihilators of simple quotients of Verma modules. Following this a characteristic variety is defined for two-sided ideals in the enveloping algebra and used to give a new and elementary proof of Duflo's ordering principle on the fibre of primitive ideals with the same central character. The main new result of this paper (Theorem 15) exhibits a decomposition of the Weyl group into disjoint subsets (cells) so that each point in a given cell defines the same ideal (via Duflo's theorem). It is conjectured that different cells correspond to different ideals, a result which would classify the primitive spectrum.