Integrable representations and the Weyl group of a Kac-Moody algebra

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


In this chapter we begin a systematic study of the Kac-Moody algebras. Recall that this is the Lie algebra g(A) associated to a generalized Cartan matrix A. The main object of the chapter is the Weyl group W of a Kac-Moody algebra, which is a generalization of the classical Weyl group in the finite-dimensional theory. However, in contrast to the finite-dimensional case, W is infinite and the union of the W-translates of the fundamental chamber is a convex cone, not the whole Cartan subalgebra h.


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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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