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Highest weight modules over the Lie algebra g(A)

  • Victor G. Kac
Part of the Progress in Mathematics book series (PM, volume 44)

Abstract

In this chapter we begin to develop the representation theory of Kac-Moody algebras. Here we introduce the so-called category O, which is roughly speaking the category of restricted h-diagonalizable modules (the precise definition is given below). We study the “elementary” objects of this category, the so-called Verma modules, and their connection with irreducible modules. We discuss the problems of irreducibility and complete reducibility in the category O. At the end of the chapter we find, as an application of the representation theory, the defining relations of Kac-Moody algebras with a symmetrizable Cartan matrix.

Keywords

High Weight Module Versus Verma Module Cartan Matrix Irreducible Module 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliographical notes and comments

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Victor G. Kac
    • 1
  1. 1.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA

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