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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Author: Dong-Uy Shin
Journal: Trans. Amer. Math. Soc. 360 (2008), 6371-6387
MSC (2000): Primary 81R50; Secondary 17B37
Published electronically: July 28, 2008
MathSciNet review: 2434291
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04446-2
PII: S 0002-9947(08)04446-2
Keywords: Highest weight crystals, generalized Kac-Moody algebras, Monster algebras
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).
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.