Abstract
The results of the last chapter can be translated into statements about the representation theory of \(\mathrm{U}(n)\). For example, we will see that each irreducible representation of \(\mathrm{U}(n)\) occurs exactly once in the decomposition of the symmetric algebra of \(V \oplus {\wedge }^{2}V\), where \(V = {\mathbb{C}}^{n}\) is the standard module of \(\mathrm{U}(n)\).
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References
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Bump, D. (2013). Some Symmetric Algebras. In: Lie Groups. Graduate Texts in Mathematics, vol 225. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8024-2_44
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DOI: https://doi.org/10.1007/978-1-4614-8024-2_44
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