## Polyhedral realization of the highest weight crystals for generalized Kac-Moody algebras

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- by Dong-Uy Shin PDF
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**360**(2008), 6371-6387 Request permission

## Abstract:

In this paper, we give a polyhedral realization of the highest weight crystals $B(\lambda )$ associated with the highest weight modules $V(\lambda )$ for the generalized Kac-Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac-Moody algebras of ranks 2, 3, and Monster algebras.## References

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## Additional Information

**Dong-Uy Shin**- Affiliation: Department of Mathematics Education, Hanyang University, Seoul 133-791, Korea
- Email: dushin@hanyang.ac.kr
- Received by editor(s): December 11, 2005
- Received by editor(s) in revised form: November 8, 2006
- Published electronically: July 28, 2008
- Additional Notes: This research was supported by the research fund of Hanyang University (HY-2007-000-0000-5889).
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 6371-6387 - MSC (2000): Primary 81R50; Secondary 17B37
- DOI: https://doi.org/10.1090/S0002-9947-08-04446-2
- MathSciNet review: 2434291