Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\) (Q1084485)
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scientific article; zbMATH DE number 3979311
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\) |
scientific article; zbMATH DE number 3979311 |
Statements
Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\) (English)
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1985
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An interesting geometric interpretation is given for the multiplicities in the decomposition of a tensor product of two irreducible finite- dimensional \({\mathfrak gl}_ n\)-modules into irreducible components. The interpretation is given in terms of some convex polyhedron in the Gel'fand-Tsetlin scheme space. An application is given to the classical Clebsch-Gordan coefficients.
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decomposition into irreducible modules
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canonical basis for \({\mathfrak gl}_ 3\)
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multiplicities
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tensor product
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\({\mathfrak gl}_ n\)-modules
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Gel'fand-Tsetlin scheme
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Clebsch-Gordan coefficients
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