Classification of Irreducible Nonzero Level Modules with Finite-Dimensional Weight Spaces for Affine Lie Algebras
Classification of Irreducible Nonzero Level Modules with Finite-Dimensional Weight Spaces for Affine Lie Algebras
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DOI：
10.1006/jabr.2000.8648
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发表时间：
2001-04
影响因子：
0.9
通讯作者：
V. Futorny;A. Tsylke
中科院分区：
文献类型：
--
作者：
V. Futorny;A. Tsylke
摘要对中心元非平凡作用于有限维权空间的不可约权仿射李代数模进行了分类。特别地，我们证明了任何这样的模都是广义Verma模的商。这种不可约模的分类被简化为A n和C n型代数的不可约无扭转模的分类，这是由于O. Mathieu（即将出版）。
Abstract We classify the irreducible weight affine Lie algebra modules with finite-dimensional weight spaces on which the central element acts nontrivially. In particular, we show that any such module is a quotient of a generalized Verma module. The classification of such irreducible modules is reduced to the classification of irreducible torsion-free modules for algebras of type A n and C n which is due to O. Mathieu (forthcoming).