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The BGG resolution, character and denominator formulas, and related results for Kac-Moody algebras

Author: Wayne Neidhardt
Journal: Trans. Amer. Math. Soc. 297 (1986), 487-504
MSC: Primary 17B67
MathSciNet review: 854079
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Abstract: Let $ \mathfrak{g}$ be a Kac-Moody algebra defined by a (not necessarily symmetrizable) generalized Cartan matrix. We construct a BGG-type resolution of the irreducible module $ L(\lambda )$ with dominant integral highest weight $ \lambda $, and we use this to obtain character and denominator formulas analogous to those of Weyl. We also determine a condition on the algebra which is sufficient for these formulas to take their classical form, and which implies that the set of defining relations is complete.

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