Abstract
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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© 1983 Springer Science+Business Media New York
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Kac, V.G. (1983). Integrable representations and the Weyl group of a Kac-Moody algebra. In: Infinite Dimensional Lie Algebras. Progress in Mathematics, vol 44. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1382-4_3
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DOI: https://doi.org/10.1007/978-1-4757-1382-4_3
Publisher Name: Birkhäuser, Boston, MA
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