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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Polyhedral realization of the highest weight crystals for generalized Kac-Moody algebras
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by Dong-Uy Shin PDF
Trans. Amer. Math. Soc. 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.
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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