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An algorithm is presented for computing the decomposition of a tensor product of two irreducible representations of a semisimple complex Lie group into its irreducible components. The algorithm uses a known formula which expresses the multiplicities of the highest weight vectors in the decomposition as an alternating sum indexed by the Weyl group. This sum… (More)
A new technique is presented for calculating the orbits of the finite Weyl group of a semisimple Lie group <italic>G</italic> in the weight lattice of <italic>G</italic>. Such calculations are important in the representation theory of <italic>G</italic>, and have previously been difficult to carry out for large Weyl groups such as… (More)