Highest Weight Modules Over Graded Lie Algebras: Resolutions, Filtrations and Character Formulas
- 1 May 1983
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 277 (1) , 133-162
- https://doi.org/10.2307/1999349
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).Keywords
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