Invariant theory, generalized Casimir operators, and tensor product decompositions of \(U(N)\) (Q2774580)
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scientific article; zbMATH DE number 1711010
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Invariant theory, generalized Casimir operators, and tensor product decompositions of \(U(N)\) |
scientific article; zbMATH DE number 1711010 |
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26 February 2002
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multiplicity problem
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tensor product
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Invariant theory, generalized Casimir operators, and tensor product decompositions of \(U(N)\) (English)
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The authors deal with the multiplicity problem, when an irreducible representation occurs more than once in the direct sum decomposition of tensor products of group representations, for \(U(N)\). They study the subspace of invariants of the space of \(r\)-fold tensor products of \(U(N)\) irreps augmented by the dual representation of the representation of interest. A way not only of computing the multiplicity, but also of constructing an orthogonal basis by using the invariant subspace that labels the multiplicity, is suggested. Examples for \(N= 3\) are given.
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