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A Formula for the Multiplicity of a Weight

  • Bertram Kostant
Chapter

Abstract

Let g be a complex semi-simple Lie algebra and h a Cartan subalgebra of g. Let ?? be an irreducible representation of g, with highest weight ?, on a finite dimensional vector space V ?. A well known theorem of E. Cartan asserts that the highest weight, ?, of ?? occurs with multiplicity one. It has been a question of long standing to determine, more generally, the multiplicity of an arbitrary weight of ??. Weyl’s formula (1.12) for the character of ?? is an expression for the function ??(?) = tr exp ??(?), ??h, on h in terms of ? and quantities independent of the representation.

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Copyright information

© Springer-Verlag New York 2009

Authors and Affiliations

  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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