Abstract
The decomposition of a product of two irreducible representations of a linear group Gl(N, ℂ) is explicitly given by the Littlewood-Richardson rule, which amounts to finding how many Young tableaux satisfy certain conditions. We obtain more general multiplicities by generating ‘vexillary’ permutations and by using partially symmetrical polynomials (Schubert polynomials).
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A la mémoire de S. Ulam, exemple et ami.
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Lascoux, A., Schützenberger, MP. Schubert polynomials and the Littlewood-Richardson rule. Lett Math Phys 10, 111–124 (1985). https://doi.org/10.1007/BF00398147
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DOI: https://doi.org/10.1007/BF00398147