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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A translation principle for Kac-Moody algebras


Author: Wayne Neidhardt
Journal: Proc. Amer. Math. Soc. 100 (1987), 395-400
MSC: Primary 17B10; Secondary 17B67
MathSciNet review: 891132
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Abstract: Let $ \mathfrak{g}$ be a Kac-Moody algebra defined by a symmetrizable generalized Cartan matrix. We show that the multiplicity of the irreducible module $ L({w_1} \cdot \lambda )$ in the Verma module $ M({w_2}\cdot\lambda )$ depends only on the elements $ {w_1}$ and $ {w_2}$ of the Weyl group, and not on the dominant integral weight $ \lambda $, generalizing the translation principle of Jantzen for finite-dimensional algebras.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0891132-6
PII: S 0002-9939(1987)0891132-6
Article copyright: © Copyright 1987 American Mathematical Society