, Volume 10, Issue 2-3, pp 111-124

Schubert polynomials and the Littlewood-Richardson rule

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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).

A la mémoire de S. Ulam, exemple et ami.