Generalized Verma Modules Induced from sl(2, C) and Associated Verma Modules
Generalized Verma Modules Induced from sl(2, C) and Associated Verma Modules
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DOI：
10.1006/jabr.2001.8815
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发表时间：
2001-08
影响因子：
0.9
通讯作者：
O. Khomenko;V. Mazorchuk
中科院分区：
文献类型：
--
作者：
O. Khomenko;V. Mazorchuk
摘要利用由具有三角分解的李代数的一个“嵌入良好”的抛物子代数导出的广义Verma模，我们自然地将同一代数上的Verma模联系起来。当抛物子代数的Levi因子的半单部分同构于sl（2，C），且广义Verma模是由无限维单模导出时，证明了相应的Verma模是单模的当且仅当原广义Verma模是单模.
Abstract With each generalized Verma module induced from a “well-embedded” parabolic subalgebra of a Lie algebra with triangular decomposition, we associate a Verma module over the same algebra in a natural way. In the case when the semisimple part of the Levi factor of the parabolic subalgebra is isomorphic to sl (2, C ) and the generalized Verma module is induced from an infinite-dimensional simple module, we prove that the associated Verma module is simple if and only if the original generalized Verma module is simple.