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Transactions of the American Mathematical Society

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



Local projective resolutions and translation functors for Kac-Moody algebras

Author: Wayne Neidhardt
Journal: Trans. Amer. Math. Soc. 305 (1988), 221-245
MSC: Primary 17B67; Secondary 17B10
MathSciNet review: 920156
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Abstract: Let $\mathfrak {g}$ be a Kac-Moody algebra defined by a not necessarily symmetrizable generalized Cartan matrix. We define translation functors and use them to show that the multiplicities $(M({w_1} \cdot \lambda ):L({w_2} \cdot \lambda ))$ are independent of the dominant integral weight $\lambda$, depending only on the elements of the Weyl group. In order to define the translation functors, we introduce the notion of local projective resolutions and use them to develop the machinery of homological algebra in certain categories of $\mathfrak {g}$-modules.

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Article copyright: © Copyright 1988 American Mathematical Society