Integrable highest weight modules: the weight system, the contravariant Hermitian form and the restriction problem

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


In this chapter we describe in detail the weight system of an integrable highest weight module L(Λ) over a Kac-Moody algebra g(A). We establish the existence of a Ii(A)-invariant positive-definite Hermitian form on L(Λ). Finally, we study the decomposition of L(Λ) with respect to various subalgebras of g(A) and derive an explicit description of the region of convergence of ch L (Λ).


Convex Hull Finite Type Inductive Assumption Hermitian Form Weight System 
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Bibliographical notes and comments

  1. Kac, V. G., Peterson, D. H. [1983 A] Infinite dimensional Lie algebras, theta functions and modular forms, Advances in Math., 50 (1983).Google Scholar
  2. Kac, V. G., Peterson, D. H:[1983 C] Unitary structure in representations of infinite-dimensional groups and a convexity theorem, MIT, preprintGoogle Scholar
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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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