Lie Groups pp 169-175 | 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  Chap. 22 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. This chapter is to some extent a continuation of the example  Chap. 19. As in that chapter, we will make many assertions that will only be proved in later chapters, mostly  Chap. 22.


Root Lattice Irreducible Representation Weyl Group Standard Representation Maximal Torus 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

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

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