Characterization of simple highest weight modules
Representation Theory
2019-08-15 v2
Abstract
We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.
Cite
@article{arxiv.1105.1123,
title = {Characterization of simple highest weight modules},
author = {Volodymyr Mazorchuk and Kaiming Zhao},
journal= {arXiv preprint arXiv:1105.1123},
year = {2019}
}