Corpus ID: 40096772

Characters of highest weight modules and integrability

@article{Dhillon2016CharactersOH,
  title={Characters of highest weight modules and integrability},
  author={Gurbir Singh Dhillon and Apoorva Khare},
  journal={arXiv: Representation Theory},
  year={2016}
}
We give positive formulas for the weights of every simple highest weight module $L(\lambda)$ over an arbitrary Kac-Moody algebra. Under a mild condition on the highest weight, we express the weights of $L(\lambda)$ as an alternating sum similar to the Weyl-Kac character formula. For general highest weight modules, we answer questions of Bump and Lepowsky on weights, and a question of Brion on the corresponding $D$-modules. Many of these results are new even in finite type. We prove similar… Expand
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