Some Symmetric Algebras
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 , Littlewood , and Macdonald .
KeywordsIrreducible Representation Standard Module Symmetric Algebra Exterior Algebra Symmetric Power
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