Shuffled Verma Modules and Principal Series Modules over Complex Semisimple Lie Algebras
Shuffled Verma Modules and Principal Series Modules over Complex Semisimple Lie Algebras
复制标题
复杂半简单李代数上的混洗 Verma 模块和主级数模块
DOI：
10.1112/jlms/s2-48.2.263
复制
发表时间：
1993
影响因子：
1.2
通讯作者：
R. Irving
中科院分区：
文献类型：
--
作者：
R. Irving
研究了复半单李代数g的主级数模的结构。通过范畴等价，这些模块可以被视为处于范畴0中，在这种伪装下，它们具有与Verma模块相同的组成因子。因此，主系列模可以被看作是混洗的Verma模，标准主系列模对应于Verma模本身。我们发现在0以内，投射不可分解模可以从混洗Verma模中构造出来，这反过来意味着某些混洗Verma模（或主级数模）具有特别简单的结构。此外，我们重新推导出过滤形式的四项精确序列的Zelebenko-Duflo-Joseph，这表明，洗牌Verma模块可以建立从Verma模块的序列的削减（继续类比与转换的扑克牌）。在导言的其余部分，我们将更详细地描述这些结果，并触及一些其他主题。
In this paper, the structure of principal series modules for a complex semisimple Lie algebra g is studied. Through a category equivalence, these modules may be viewed as lying in the category 0, in which guise they have the same composition factors as Verma modules. Thus principal series modules may be viewed as shuffled Verma modules, with the standard principal series modules corresponding to the Verma modules themselves. We find within 0 that projective indecomposable modules can be built out of shuffled Verma modules, which in turn implies that certain shuffled Verma modules (or principal series modules) have a particularly simple structure. In addition, we re-derive in a filtered form the four-term exact sequence of Zelebenko-Duflo-Joseph, which shows that shuffled Verma modules can be built from Verma modules by a sequence of cuts (to continue the analogy with transformations of decks of cards). In the remainder of the introduction, we describe these results in more detail, and touch on some additional themes.