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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas


Authors: Alvany Rocha-Caridi and Nolan R. Wallach
Journal: Trans. Amer. Math. Soc. 277 (1983), 133-162
MSC: Primary 17B10; Secondary 17B65, 17B70
MathSciNet review: 690045
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Abstract: In this paper the study of multiplicities in Verma modules for Kac-Moody algebras is initiated. Our analysis comprises the case when the integral root system is Euclidean of rank two. Complete results are given in the case of rank two, Kac-Moody algebras, affirming the Kazhdan-Lusztig conjectures for the case of infinite dihedral Coxeter groups.

The main tools in this paper are the resolutions of standard modules given in [21] and a generalization to the case of Kac-Moody Lie algebras of Jantzen's character sum formula for a quotient of two Verma modules (one of the main results of this article).

Finally, a precise analogy is drawn between the rank two, Kac-Moody algebras and the Witt algebra (the Lie algebra of vector fields on the circle).


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DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0690045-3
PII: S 0002-9947(1983)0690045-3
Article copyright: © Copyright 1983 American Mathematical Society