Lie Groups pp 157-161 | Cite as

Highest-Weight Vectors

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


If G is a compact connected Lie group, we will show in Chapter 25 that its irreducible representations are parametrized uniquely by their highest-weight vectors. In this chapter, we will explain what this means and give some illustrative examples. The proofs will be postponed until later chapters, mostly Chapter 25.


Irreducible Representation Weyl Group Standard Representation Weight Lattice Irreducible Constituent 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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