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 be a Kac-Moody algebra defined by a (not necessarily symmetrizable) generalized Cartan matrix. We construct a BGG-type resolution of the irreducible module with dominant integral highest weight , 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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DOI:
https://doi.org/10.1090/S0002-9947-1986-0854079-0

Article copyright:
© Copyright 1986
American Mathematical Society