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Transactions of the American Mathematical Society

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

 

 

Kazhdan-Lusztig conjecture for generalized Kac-Moody algebras. II. Proof of the conjecture


Author: Satoshi Naito
Journal: Trans. Amer. Math. Soc. 347 (1995), 3891-3919
MSC: Primary 17B67; Secondary 17B10
MathSciNet review: 1316859
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Abstract: Generalized Kac-Moody algebras were introduced by Borcherds in the study of Conway and Norton's moonshine conjectures for the Monster sporadic simple group. In this paper, we prove the Kazhdan-Lusztig conjecture for generalized Kac-Moody algebras under a certain mild condition, by using a generalization (to the case of generalized Kac-Moody algebras) of Jantzen's character sum formula. Our (main) formula generalizes the celebrated result for the case of Kac-Moody algebras, and describes the characters of irreducible highest weight modules over generalized Kac-Moody algebras in terms of the "extended" Kazhdan-Lusztig polynomials.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1316859-2
Keywords: Generalized Kac-Moody algebra, character formula, Kazhdan-Lusztig conjecture
Article copyright: © Copyright 1995 American Mathematical Society