Polyhedra in the scheme space and the canonical basis in irreducible representations of \({\mathfrak gl}_ 3\)
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.
canonical basis for \({\mathfrak gl}_ 3\)
scientific article; zbMATH DE number 3979311