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Journal of the London Mathematical Society Advance Access published online on December 13, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm094
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© 2007 London Mathematical Society

Polyhedral realization of crystal bases for generalized Kac--Moody algebras

Dong-Uy Shin

Department of Mathematics Education
Hanyang University
Seoul 133-791
Korea

In this paper, we give a polyhedral realization of the crystal B({infty}) of Uq–(g) for the generalized Kac–Moody algebras. As applications, we give explicit descriptions of crystals for the generalized Kac–Moody algebras of rank 2 and 3, and Monster Lie algebras.

This research was supported by KRF Grant #2007-331-C00007.

2000 Mathematics Subject Classification 81R50 (primary), 17B37 (secondary).

Received June 19, 2006; revised March 14, 2007;
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