Lie Groups pp 370-374 | Cite as

Some Symmetric Algebras

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


The results of the last chapter can be translated into statements about the representation theory of U(n). For example, we will see that every irreducible representation of U(n) occurs exactly once in the decomposition of the symmetric algebra of V⊕⋀2 V, where V = ℂ n is the standard module of U(n). The results of this chapter are also proved in Goodman and Wallach [47], Littlewood [93], and Macdonald [95].


Irreducible Representation Standard Module Symmetric Algebra Exterior Algebra Symmetric Power 
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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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