Abstract
The Bernstein—Gelfand—Gelfand category CQ is defined and its various basic properties are established (including the characterization of irreducible objects in as irreducible quotients of Verma modules and characterization of integrable modules in 0) in Section 2.1. For any dominant integral weight X, an integrable highest weight g-module Lm’(X) is explicitly constructed, and it is shown that any integrable highest weight g-module is a quotient of Lm’ (X) An explicit expression for the action of the Casimir—Kac element (in the symmetrizable case)on any Verma module is obtained
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© 2002 Springer Science+Business Media New York
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Kumar, S. (2002). Representation Theory of Kac-Moody Algebras. In: Kac-Moody Groups, their Flag Varieties and Representation Theory. Progress in Mathematics, vol 204. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0105-2_2
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DOI: https://doi.org/10.1007/978-1-4612-0105-2_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6614-3
Online ISBN: 978-1-4612-0105-2
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