On the Reducibility of Scalar Generalized Verma Modules of Abelian Type
On the Reducibility of Scalar Generalized Verma Modules of Abelian Type
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DOI：
10.1007/s10468-015-9567-2
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发表时间：
2015-01
影响因子：
0.6
通讯作者：
Haian He
中科院分区：
文献类型：
--
作者：
Haian He
复半单李代数的抛物子代数称为阿贝尔型抛物子代数，如果它的幂零根是阿贝尔根。本文给出了Abel类抛物子代数上的标量广义Verma模的参数的一个完全刻画，使得这些模是可约的。证明使用了Jantzen的简单性准则，以及么正最高权模的Enright-Howe-Wallach分类。
A parabolic subalgebraof a complex semisimple Lie algebrais called a parabolic subalgebra of abelian type if its nilpotent radical is abelian. In this paper, we provide a complete characterization of the parameters for scalar generalized Verma modules attached to parabolic subalgebras of abelian type such that the modules are reducible. The proofs use Jantzen’s simplicity criterion, as well as the Enright-Howe-Wallach classification of unitary highest weight modules.