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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

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Highest weight modules over graded Lie algebras: resolutions, filtrations and character formulas
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by Alvany Rocha-Caridi and Nolan R. Wallach PDF
Trans. Amer. Math. Soc. 277 (1983), 133-162 Request permission

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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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 277 (1983), 133-162
  • MSC: Primary 17B10; Secondary 17B65, 17B70
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0690045-3
  • MathSciNet review: 690045